ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 25 Jul 2024 01:20:27 GMT2024-07-25T01:20:27Z50431- Self-normalized moderate deviations for independent random variableshttps://scholarbank.nus.edu.sg/handle/10635/105350Title: Self-normalized moderate deviations for independent random variables
Authors: Jing, B.Y.; Liang, H.Y.; Zhou, W.
Abstract: Let X 1,X 2,... be a sequence of independent random variables (r. v. s) belonging to the domain of attraction of a normal or stable law. In this paper, we study moderate deviations for the self-normalized sum Σ i=1 nX i/V n,p where V n,p = (Σ i=1 n{pipe}X i{pipe} p) 1/p (p > 1). Applications to the self-normalized law of the iterated logarithm, Studentized increments of partial sums, t-statistic, and weighted sum of independent and identically distributed (i. i. d.) r. v. s are considered. © 2012 Science China Press and Springer-Verlag Berlin Heidelberg.
Sun, 01 Jan 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1053502012-01-01T00:00:00Z
- Saddlepoint approximation for sample quantiles with some applicationshttps://scholarbank.nus.edu.sg/handle/10635/105343Title: Saddlepoint approximation for sample quantiles with some applications
Authors: Zhu, J.; Zhou, W.
Abstract: In this article, we use the integral form of the binomial distribution to derive saddlepoint approximations for sample quantiles. As an application, we present the calculation of the tail probability of the empirical log-likelihood ratio statistic for quantiles. Simulation results are also given to show that our approximations are extremely accurate.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1053432009-01-01T00:00:00Z
- Saddlepoint approximations for studentized compound Poisson sums with no moment conditions in audit samplinghttps://scholarbank.nus.edu.sg/handle/10635/105345Title: Saddlepoint approximations for studentized compound Poisson sums with no moment conditions in audit sampling
Authors: Zhou, G.L.; Zhou, W.
Abstract: Saddlepoint approximations for the studentized compound Poisson sums with no moment conditions in audit sampling are derived. This result not only provides a very accurate approximation for studentized compound Poisson sums, but also can be applied much more widely in statistical inference of the error amount in an audit population of accounts to check the validity of financial statements of a firm. Some numerical illustrations and comparison with the normal approximation method are presented. © 2010 Science China Press and Springer-Verlag Berlin Heidelberg.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1053452011-01-01T00:00:00Z
- Uniformly bounded components of normalityhttps://scholarbank.nus.edu.sg/handle/10635/105452Title: Uniformly bounded components of normality
Authors: Wang, X.; Zhou, W.
Abstract: Suppose that f(z) is a transcendental entire function and that the Fatou set F(f) ‡ ∅. Set B1(f):=supU sup z∈U log(|z| + 3)/infw∈U log(|w| + 3) and B 2(f):=supU supz∈U log(|z| + 30)/inf w∈U log(|w| + 3), where the supremum supU is taken over all components of F(f). If B1(f) < ∞ or B 2(f) < ∞, then we say F(f) is strongly uniformly bounded or uniformly bounded respectively. We show that, under some conditions, F(f) is (strongly) uniformly bounded. © 2007 Cambridge Philosophical Society.
Sun, 01 Jul 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1054522007-07-01T00:00:00Z
- Tracy-Widom law for the extreme eigenvalues of sample correlation matriceshttps://scholarbank.nus.edu.sg/handle/10635/105441Title: Tracy-Widom law for the extreme eigenvalues of sample correlation matrices
Authors: Bao, Z.; Pan, G.; Zhou, W.
Abstract: Let the sample correlation matrix be W = YY Twhere Y = (y ij) p;n with y ij. We assume to be a collection of independent symmetrically distributed random variables with sub-exponential tails. Moreover, for any i, we assume x ij, 1 ≤ j ≤ n to be identically distributed. We assume 0 < p < n and p=n → y with some y ε (0; 1) as p; n → ∞. In this paper, we provide the Tracy-Widom law (TW1) for both the largest and smallest eigenvalues of W. If x ij are i.i.d. standard normal, we can derive the TW 1 for both the largest and smallest eigenvalues of the matrix R = RR T, where R = (r ij) p;n with r ij.
Sun, 01 Jan 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1054412012-01-01T00:00:00Z
- Towards a universal self-normalized moderate deviationhttps://scholarbank.nus.edu.sg/handle/10635/105440Title: Towards a universal self-normalized moderate deviation
Authors: Jing, B.-Y.; Shao, Q.-M.; Zhou, W.
Abstract: This paper is an attempt to establish a universal moderate deviation for self-normalized sums of independent and identically distributed random variables without any moment condition. The exponent term in the moderate deviation is specified when the distribution is in the centered Feller class. An application to the law of the iterated logarithm is given. © 2008 American Mathematical Society.
Fri, 01 Aug 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1054402008-08-01T00:00:00Z
- Statistical inference for P (X < Y)https://scholarbank.nus.edu.sg/handle/10635/105391Title: Statistical inference for P (X < Y)
Authors: Zhou, W.
Abstract: Let X and Y be two independent continuous random variables. We make statistical inference about θ=P(X
Wed, 30 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1053912008-01-30T00:00:00Z
- SLE curves and natural parametrizationhttps://scholarbank.nus.edu.sg/handle/10635/105371Title: SLE curves and natural parametrization
Authors: Lawler, G.F.; Zhou, W.
Abstract: Developing the theory of two-sided radial and chordal SLE, we prove that the natural parametrization on SLEκ curves is well defined for all κ < 8. Our proof uses a two-interior-point local martingale. © Institute of Mathematical Statistics, 2013.
Wed, 01 May 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1053712013-05-01T00:00:00Z
- Tail probability approximations for Student's t-statisticshttps://scholarbank.nus.edu.sg/handle/10635/105398Title: Tail probability approximations for Student's t-statistics
Authors: Zhou, W.; Jing, B.-Y.
Abstract: In this paper, we derive saddlepoint approximations for Student's t-statistics for strongly nonlattice random variables without moment conditions. Under very mild conditions, we show that saddlepoint equations always have solutions. © Springer-Verlag Berlin Heidelberg 2006.
Fri, 01 Dec 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1053982006-12-01T00:00:00Z
- Asymptotic distribution of the largest off-diagonal entry of correlation matriceshttps://scholarbank.nus.edu.sg/handle/10635/105020Title: Asymptotic distribution of the largest off-diagonal entry of correlation matrices
Authors: Zhou, W.
Abstract: Suppose that we have n observations from a p-dimensional population. We are interested in testing that the p variates of the population are independent under the situation where p goes to infinity as n → ∞. A test statistic is chosen to be Ln = max1≤i
Thu, 01 Nov 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050202007-11-01T00:00:00Z
- A note on edgeworth expansions for U-statistics under minimal conditionshttps://scholarbank.nus.edu.sg/handle/10635/104954Title: A note on edgeworth expansions for U-statistics under minimal conditions
Authors: Jing, B.-Y.; Zhou, W.
Abstract: A one-term Edgeworth expansion for U-statistics with kernel h(x, y) was derived by Jing and Wang [3] under optimal moment conditions. In this note, we show that one of the optimal moment conditions E| h(X 1, X 2|5/3 < ∞ can be weakened to lim t→∞ t 5/3 P(|h(X 1, X 2)| > t) → 0. © 2005 Springer Science+Business Media, Inc.
Fri, 01 Jul 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1049542005-07-01T00:00:00Z
- A note on rate of convergence in probability to semicircular lawhttps://scholarbank.nus.edu.sg/handle/10635/104955Title: A note on rate of convergence in probability to semicircular law
Authors: Bai, Z.; Hu, J.; Pan, G.; Zhou, W.
Abstract: In the present paper, we prove that under the assumption of the finite sixth moment for elements of a Wigner matrix, the convergence rate of its empirical spectral distribution to the Wigner semicircular law in probability is O(n-1/2) when the dimension n tends to infinity.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1049552011-01-01T00:00:00Z
- Almost sure limit of the smallest eigenvalue of some sample correlation matriceshttps://scholarbank.nus.edu.sg/handle/10635/104988Title: Almost sure limit of the smallest eigenvalue of some sample correlation matrices
Authors: Xiao, H.; Zhou, W.
Abstract: Let X(n) = (Xij) be a p × n data matrix, where the n columns form a random sample of size n from a certain p-dimensional distribution. Let R(n) = (ρij) be the p × p sample correlation coefficient matrix of X(n), and S(n) = (1/n)X(n)(X(n))*-X̄X̄* be the sample covariance matrix of X(n), where X̄ is the mean vector of the n observations. Assuming that Xij are independent and identically distributed with finite fourth moment, we show that the smallest eigenvalue of R(n) converges almost surely to the limit (1-√c)2 as n → ∞ and p/n → c ∈ (0,∞). We accomplish this by showing that the smallest eigenvalue of S(n) converges almost surely to (1-√c)2. © Springer Science+Business Media, LLC 2009.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1049882010-01-01T00:00:00Z
- On normal approximations to U -statisticshttps://scholarbank.nus.edu.sg/handle/10635/105261Title: On normal approximations to U -statistics
Authors: Bentkus, V.; Jing, B.-Y.; Zhou, W.
Abstract: Let X1,..., Xn be i.i.d. random observations. Let S{double-struck} = L{double-struck} + T{double-struck} be a U -statistic of order k ≥ 2 where L{double-struck} is a linear statistic having asymptotic normal distribution, and T{double-struck} is a stochastically smaller statistic. We show that the rate of convergence to normality for S{double-struck} can be simply expressed as the rate of convergence to normality for the linear part L{double-struck} plus a correction term, (var T{double-struck}) ln2(var T{double-struck}), under the condition E{double-struck}T{double-struck}2 < ∞. An optimal bound without this log factor is obtained under a lower moment assumption E{double-struck}|T{double-struck}|α < ∞ for α
Sun, 01 Nov 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052612009-11-01T00:00:00Z
- Nonparametric statistical inference for P(Xhttps://scholarbank.nus.edu.sg/handle/10635/105244Title: Nonparametric statistical inference for P(X
Authors: Guangming, P.; Xiping, W.; Wang, Z.
Abstract: Let X, Y and Z be three independent random variables from three different populations. The stress-strength model P(X < Y < Z), the volume under the three-class ROC surface, has extensive applications in various areas since it provides a global measure of differences between or among populations. In this paper, we suggest to make statistical inference for P(X < Y < Z) via two methods, the nonparametric normal approximation and the jackknife empirical likelihood, since the usual empirical likelihood method for U-statistics is too complicated to apply. The results of the simulation studies indicate that these two methods work promisingly compared to other existing methods. Some classical and real data sets were analyzed using these two proposed methods. Practically, for simplicity, the nonparametric normal approximation method should be preferred; for better statistical results, one is suggested to use the JEL method although it is more complex than the normal approximation one. © 2013, Indian Statistical Institute.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052442013-01-01T00:00:00Z
- Circular law, extreme singular values and potential theoryhttps://scholarbank.nus.edu.sg/handle/10635/105055Title: Circular law, extreme singular values and potential theory
Authors: Pan, G.; Zhou, W.
Abstract: Consider the empirical spectral distribution of complex random n × n matrix whose entries are independent and identically distributed random variables with mean zero and variance 1 / n. In this paper, via applying potential theory in the complex plane and analyzing extreme singular values, we prove that this distribution converges, with probability one, to the uniform distribution over the unit disk in the complex plane, i.e. the well known circular law, under the finite fourth moment assumption on matrix elements. © 2009 Elsevier Inc. All rights reserved.
Mon, 01 Mar 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050552010-03-01T00:00:00Z
- Asymptotic properties of nonparametric frontier estimatorshttps://scholarbank.nus.edu.sg/handle/10635/105027Title: Asymptotic properties of nonparametric frontier estimators
Authors: Horváth, L.; Horváth, Z.; Zhou, W.
Abstract: Aragon, Daouia, and Thomas-Agnan (2005, Econometric Theory 21, 358-389) introduced a new nonparametric frontier estimation. We prove the weak convergence of the empirical conditional quantile function. The distribution of the limit depends on the unknown conditional quantile density function. We provide a method to construct uniform confidence bands without estimating the conditional quantile density. © 2008 Cambridge University Press.
Mon, 01 Dec 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050272008-12-01T00:00:00Z
- Confidence bands for ROC curveshttps://scholarbank.nus.edu.sg/handle/10635/105067Title: Confidence bands for ROC curves
Authors: Horváth, L.; Horváth, Z.; Zhou, W.
Abstract: We develop two methods to construct confidence bands for the receiver operating characteristic (ROC) curve without estimating the densities of the underlying distributions. The first method is based on the smoothed bootstrap while the second method uses the Bonferroni inequality. As an illustration, we provide confidence bands for the ROC curve using data on Duchanne Muscular Dystrophy. © 2007 Elsevier B.V. All rights reserved.
Tue, 01 Jul 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050672008-07-01T00:00:00Z
- Convergence rates to the Marchenko-Pastur type distributionhttps://scholarbank.nus.edu.sg/handle/10635/105073Title: Convergence rates to the Marchenko-Pastur type distribution
Authors: Bai, Z.; Hu, J.; Zhou, W.
Abstract: S n = 1 n T 1/2 n X nX n T 1/2 n , where X n = (xi j ) is a p n matrix consisting of independent complex entries with mean zero and variance one, Tn is a p p nonrandom positive definite Hermitian matrix with spectral norm uniformly bounded in p. In this paper, if supn supi, j E | x 8 i j |> ∞ and y n = p/n > 1 uniformly as n → ∞, we obtain that the rate of the expected empirical spectral distribution of Sn converging to its limit spectral distribution is O(n 1/2). Moreover, under the same assumption, we prove that for any < 0, the rates of the convergence of the empirical spectral distribution of Sn in probability and the almost sure convergence are O(n 2/5) and O(n 2/5+) respectively. © 2011 Elsevier B.V. All rights reserved.
Sun, 01 Jan 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050732012-01-01T00:00:00Z
- Functional CLT for sample covariance matriceshttps://scholarbank.nus.edu.sg/handle/10635/105154Title: Functional CLT for sample covariance matrices
Authors: Bai, Z.; Wang, X.; Zhou, W.
Abstract: Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including [(1 - √ y)2, (1 + √ y)2], the support of the Marčenko-Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions. © 2010 ISI/BS.
Mon, 01 Nov 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051542010-11-01T00:00:00Z
- Limiting distributions of the non-central t-statistic and their applications to the power of t-tests under non-normalityhttps://scholarbank.nus.edu.sg/handle/10635/105198Title: Limiting distributions of the non-central t-statistic and their applications to the power of t-tests under non-normality
Authors: Bentkus, V.; Jing, B.-Y.; Shao, Q.-M.; Zhou, W.
Abstract: Let X1, X2,... be a sequence of independent and identically distributed random variables. Let X be an independent copy of X1. Define Tn = √nX/S, where X and S2 are the sample mean and the sample variance, respectively. We refer to Tn as the central or non-central (Student's) t-statistic, depending on whether EX = 0 or EX ≠ 0, respectively. The non-central t-statistic arises naturally in the calculation of powers for t-tests. The central t-statistic has been well studied, while there is a very limited literature on the non-central t-statistic. In this paper, we attempt to narrow this gap by studying the limiting behaviour of the non-central t-statistic, which turns out to be quite complicated. For instance, it is well known that, under finite second-moment conditions, the limiting distributions for the central t-statistic are normal while those for the non-central t-statistic can be non-normal and can critically depend on whether or not EX4 = ∞. As an application, we study the effect of non-normality on the performance of the t-test. © 2007 ISI/BS.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051982007-01-01T00:00:00Z
- Jackknife empirical likelihood method for case-control studies with gene-environment independence on controlshttps://scholarbank.nus.edu.sg/handle/10635/105188Title: Jackknife empirical likelihood method for case-control studies with gene-environment independence on controls
Authors: Jing, B.-Y.; Li, Z.; Qin, J.; Zhou, W.
Abstract: In this paper, we propose a jackknife empirical likelihood method to do inference for the interested parameters of the multiplicative-intercept risk models by taking into account the gene-environment independence on controls in case-control studies. It is shown that the proposed statistic is asymptotically chi-squared distributed. Simulation studies investigate the small-sample properties. A real example is also given.
Sun, 01 Jan 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051882012-01-01T00:00:00Z
- Jackknife empirical likelihoodhttps://scholarbank.nus.edu.sg/handle/10635/105187Title: Jackknife empirical likelihood
Authors: Jing, B.-Y.; Yuan, J.; Zhou, W.
Abstract: Empirical likelihood has been found very useful in many different occasions. However, when applied directly to some more complicated statistics such as U-statistics, it runs into serious computational difficulties. In this paper, we introduce a so-called jackknife empirical likelihood (JEL) method. The new method is extremely simple to use in practice. In particular, the JEL is shown to be very effective in handling one and two-sample U-statistics. The JEL can be potentially useful for other nonlinear statistics. © 2009 American Statistical Association.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051872009-01-01T00:00:00Z
- Large sample covariance matrices without independence structures in columnshttps://scholarbank.nus.edu.sg/handle/10635/105190Title: Large sample covariance matrices without independence structures in columns
Authors: Bai, Z.; Zhou, W.
Abstract: The limiting spectral distribution of large sample covariance matrices is derived under dependence conditions. As applications, we obtain the limiting spectral distributions of Spearman's rank correlation matrices, sample correlation matrices, sample covariance matrices from finite populations, and sample covariance matrices from causal AR(1) models.
Tue, 01 Apr 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051902008-04-01T00:00:00Z
- Nonparametric estimate of spectral density functions of sample covariance matrices: A first stephttps://scholarbank.nus.edu.sg/handle/10635/105240Title: Nonparametric estimate of spectral density functions of sample covariance matrices: A first step
Authors: Jing, B.-Y.; Pan, G.; Shao, Q.-M.; Zhou, W.
Abstract: The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown.We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the performance of the estimators. © Institute of Mathematical Statistics, 2010.
Wed, 01 Dec 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052402010-12-01T00:00:00Z
- New estimators of spectral distributions of Wigner matriceshttps://scholarbank.nus.edu.sg/handle/10635/105236Title: New estimators of spectral distributions of Wigner matrices
Authors: Zhou, W.
Abstract: We introduce kernel estimators for the semi-circular law. In this first part of our general theory on the estimators, we prove the consistency and conduct simulation study to show the performance of the estimators. We also point out that Wigner's semi-circular law for our new estimators and the classical empirical spectral distributions is still true when the elements of Wigner matrices do not have finite variances but are in the domain of attraction of normal law. © 2013 American Institute of Physics.
Wed, 06 Mar 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052362013-03-06T00:00:00Z
- Empirical likelihood for least absolute relative error regressionhttps://scholarbank.nus.edu.sg/handle/10635/125052Title: Empirical likelihood for least absolute relative error regression
Authors: Li, Z.; Lin, Y.; Zhou, G.; Zhou, W.
Abstract: Multiplicative regression models are useful for analyzing data with positive responses, such as wages, stock prices and lifetimes, that are particularly common in economic, financial, epidemiological and social studies. Recently, the least absolute relative error (LARE) estimation was proposed to be a useful alternative to the conventional least squares (LS) or least absolute deviation (LAD). However, one may resort to the time-consuming resampling methods for the inference of the LARE estimation. This paper proposes an empirical likelihood approach towards constructing confidence intervals/regions of the regression parameters for the multiplicative models. The major advantage of the proposal is its ability of internal studentizing to avoid density estimation. And it is computationally fast. Simulation studies investigate the effectiveness of the proposed method. An analysis of the body fat data is presented to illustrate the new method. © 2013 Sociedad de Estadística e Investigación Operativa.
Wed, 01 Jan 2014 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1250522014-01-01T00:00:00Z
- Empirical Likelihood for Compound Poisson Processeshttps://scholarbank.nus.edu.sg/handle/10635/105116Title: Empirical Likelihood for Compound Poisson Processes
Authors: Li, Z.; Wang, X.; Zhou, W.
Abstract: Summary: Let {N(t), t > 0} be a Poisson process with rate λ > 0, independent of the independent and identically distributed random variables X1,X2,... with mean μ and variance σ2. The stochastic process ∑j=1 N(t)Xj is then called a compound Poisson process and has a wide range of applications in, for example, physics, mining, finance and risk management. Among these applications, the average number of objects, which is defined to be λμ, is an important quantity. Although many papers have been devoted to the estimation of λμ in the literature, in this paper, we use the well-known empirical likelihood method to construct confidence intervals. The simulation results show that the empirical likelihood method often outperforms the normal approximation and Edgeworth expansion approaches in terms of coverage probabilities. A real data set concerning coal-mining disasters is analyzed using these methods. © 2012 Australian Statistical Publishing Association Inc. Published by Wiley Publishing Asia Pty Ltd.
Sat, 01 Dec 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051162012-12-01T00:00:00Z
- Empirical likelihood for non-degenerate U-statisticshttps://scholarbank.nus.edu.sg/handle/10635/105117Title: Empirical likelihood for non-degenerate U-statistics
Authors: Jing, B.-Y.; Yuan, J.; Zhou, W.
Abstract: Standard empirical likelihood for U-statistics is too computationally expensive. To overcome this computational difficulty, we reformulate the non-degenerate U-statistics as a sample mean of some "pseudo" observations in this paper, and show that the empirical log-likelihood ratio has an asymptotic chi-squared distribution under the second moment condition. The method is extremely simple to use, and yet provide better coverage accuracy in general than other alternative methods from our simulation studies. © 2007 Elsevier B.V. All rights reserved.
Tue, 15 Apr 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051172008-04-15T00:00:00Z
- Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communicationshttps://scholarbank.nus.edu.sg/handle/10635/105024Title: Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications
Authors: Pan, G.-M.; Guo, M.-H.; Zhou, W.
Abstract: Let sk = 1/√N (v1k,...,vNk) T, k = 1,..., K, where [vik, i, k = 1,...} are independent and identically distributed random variables with Ev11 =0 and Ev 11 2 = 1. Let Sk = (S1,...,s k-1, sk+1,...,sK), Pk = diag(p 1,..., pk-1, pk+1,...,pK) and βk = pksk T(SkP kSk T + σ2I)-1 sk, where pk ≥ 0 and the βk is referred to as the signal-to-interference ratio (SIR) of user k with linear minimum mean-square error (LMMSE) detection in wireless communications. The joint distribution of the SIRs for a finite number of users and the empirical distribution of all users' SIRs are both investigated in this paper when K and N tend, to infinity with the limit of their ratio being positive constant. Moreover, the sum of the SIRs of all users, after subtracting a proper value, is shown to have a Gaussian limit. © Institute of Mathematical Statistics, 2007.
Thu, 01 Feb 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050242007-02-01T00:00:00Z
- Central limit theorem for signal-to-interference ratio of reduced rank linear receiverhttps://scholarbank.nus.edu.sg/handle/10635/105049Title: Central limit theorem for signal-to-interference ratio of reduced rank linear receiver
Authors: Pan, G.M.; Zhou, W.
Abstract: Let sk = 1/√N (v1k, . . . ,vNk) T, with {vik, i, k = 1, . . .} independent and identically distributed complex random variables. Write Sk = (s1, . . . , sk-1, sk+1, . . ,sK) Pk =diag(p1, . . . ,pk-1, pk+1, . . . ,p K), Rk = (SkPk Sk* + σ2I) and Akm = [sk, Rks k, . . . ,Rk m-1sk]. Define βkm = pksk*Akm (A km* × RkAkm)-11 A km*sk, referred to as the signal-to-interference ratio (SIR) of user k under the multistage Wiener (MSW) receiver in a wireless communication system. It is proved that the output SIR under the MSW and the mutual information statistic under the matched filter (MF) are both asymptotic Gaussian when N/ K → c >0. Moreover, we provide a central limit theorem for linear spectral statistics of eigenvalues and eigenvectors of sample covariance matrices, which is a supplement of Theorem 2 in Bai, Miao and Pan [Ann. Probab. 35 (2007) 1532-1572]. And we also improve Theorem 1.1 in Bai and Silverstein [Ann. Probab. 32 (2004) 553-605]. © Institute of Mathematical. Statistics, 2008.
Sun, 01 Jun 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050492008-06-01T00:00:00Z
- CLT for linear spectral statistics of Wigner matriceshttps://scholarbank.nus.edu.sg/handle/10635/105058Title: CLT for linear spectral statistics of Wigner matrices
Authors: Bai, Z.; Wang, X.; Zhou, W.
Abstract: In this paper, we prove that the spectral empirical process of Wigner matrices under sixthmoment conditions, which is indexed by a set of functions with continuous fourth-order derivatives on an open interval including the support of the semicircle law, converges weakly in finite dimensions to a Gaussian process.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050582009-01-01T00:00:00Z
- Central Limit Theorem for Partial Linear Eigenvalue Statistics of Wigner Matriceshttps://scholarbank.nus.edu.sg/handle/10635/105048Title: Central Limit Theorem for Partial Linear Eigenvalue Statistics of Wigner Matrices
Authors: Bao, Z.; Pan, G.; Zhou, W.
Abstract: In this paper, we study the complex Wigner matrices Mn=1/√n Wn whose eigenvalues are typically in the interval [-2,2]. Let λ1≤λ2⋯≤λn be the ordered eigenvalues of Mn. Under the assumption of four matching moments with the Gaussian Unitary Ensemble (GUE), for test function f 4-times continuously differentiable on an open interval including [-2,2], we establish central limit theorems for two types of partial linear statistics of the eigenvalues. The first type is defined with a threshold u in the bulk of the Wigner semicircle law as An[f; u]=∑l=1 nf(λl)1{λl≤u}. And the second one is Bn[f; k]=∑l=1 kf(λl) with positive integer k=kn such that k/n→y∈(0,1) as n tends to infinity. Moreover, we derive a weak convergence result for a partial sum process constructed from Bn[f; ⌊ nt⌋]. The main difficulty is to deal with the linear eigenvalue statistics for the test functions with several non-differentiable points. And our main strategy is to combine the Helffer-Sjöstrand formula and a comparison procedure on the resolvents to extend the results from GUE case to general Wigner matrices case. Moreover, the results on An[f;u] for the real Wigner matrices will also be briefly discussed. © 2012 Springer Science+Business Media New York.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050482013-01-01T00:00:00Z
- Central limit theorem for Hotelling's t2 statistic under large dimensionhttps://scholarbank.nus.edu.sg/handle/10635/105047Title: Central limit theorem for Hotelling's t2 statistic under large dimension
Authors: Pan, G.M.; Zhou, W.
Abstract: In this paper we prove the central limit theorem for Hotelling's T 2 statistic when the dimension of the random vectors is proportional to the sample size. © 2011 Institute of Mathematical Statistics.
Sat, 01 Oct 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050472011-10-01T00:00:00Z
- Boundary proximity of SLEhttps://scholarbank.nus.edu.sg/handle/10635/105043Title: Boundary proximity of SLE
Authors: Schramm, O.; Zhou, W.
Abstract: This paper examines how close the chordal SLEK curve gets to the real line asymptotically far away from its starting point. In particular, when K ε (0, 4), it is shown that if β > β K:= 1/(8/K - 2), then the intersection of the SLEK curve with the graph of the function y = x/(log x)β, x > e, is a.s. bounded, while it is a.s. unbounded if β = βK. The critical SLE4 curve a.s. intersects the graph of x > ee, in an unbounded set if α ≤ 1, but not if α > 1. Under a very mild regularity assumption on the function y(x), we give a necessary and sufficient integrability condition for the intersection of the SLEK path with the graph of y to be unbounded. When the intersection is bounded a.s., we provide an estimate for the probability that the SLEK path hits the graph of y. We also prove that the Hausdorff dimension of the intersection set of the SLEK curve and the real axis is 2 - 8/K when 4 < K < 8. © Springer-Verlag 2008.
Tue, 01 Dec 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1050432009-12-01T00:00:00Z
- Saddlepoint approximation for student's t-statistic with no moment conditionshttps://scholarbank.nus.edu.sg/handle/10635/53146Title: Saddlepoint approximation for student's t-statistic with no moment conditions
Authors: Jing, B.-Y.; Shao, Q.-M.; Zhou, W.
Abstract: A saddlepoint approximation of the Student's t-statistic was derived by Daniels and Young [Biometrika 78 (1991) 169-179] under the very stringent exponential moment condition that requires that the underlying density function go down at least as fast as a Normal density in the tails. This is a severe restriction on the approximation's applicability. In this paper we show that this strong exponential moment restriction can be completely dispensed with, that is, saddlepoint approximation of the Student's t-statistic remains valid without any moment condition. This confirms the folklore that the Student's t-statistic is robust against outliers. The saddlepoint approximation not only provides a very accurate approximation for the Student's t-statistic, but it also can be applied much more widely in statistical inference. As a result, saddlepoint approximations should always be used whenever possible. Some numerical work will be given to illustrate these points. © Institute of Mathematical Statistics, 2004.
Wed, 01 Dec 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/531462004-12-01T00:00:00Z
- On SURE-Type Double Shrinkage Estimationhttps://scholarbank.nus.edu.sg/handle/10635/141002Title: On SURE-Type Double Shrinkage Estimation
Authors: Bing-Yi Jing; Zhouping Li; Guangming Pan; Wang Zhou
Wed, 25 Jan 2017 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1410022017-01-25T00:00:00Z
- Saddlepoint approximation for student's t-statistic with no moment conditionshttps://scholarbank.nus.edu.sg/handle/10635/104074Title: Saddlepoint approximation for student's t-statistic with no moment conditions
Authors: Jing, B.-Y.; Shao, Q.-M.; Zhou, W.
Abstract: A saddlepoint approximation of the Student's t-statistic was derived by Daniels and Young [Biometrika 78 (1991) 169-179] under the very stringent exponential moment condition that requires that the underlying density function go down at least as fast as a Normal density in the tails. This is a severe restriction on the approximation's applicability. In this paper we show that this strong exponential moment restriction can be completely dispensed with, that is, saddlepoint approximation of the Student's t-statistic remains valid without any moment condition. This confirms the folklore that the Student's t-statistic is robust against outliers. The saddlepoint approximation not only provides a very accurate approximation for the Student's t-statistic, but it also can be applied much more widely in statistical inference. As a result, saddlepoint approximations should always be used whenever possible. Some numerical work will be given to illustrate these points. © Institute of Mathematical Statistics, 2004.
Wed, 01 Dec 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1040742004-12-01T00:00:00Z
- High Dimensional Elliptical Sliced Inverse Regression in non-Gaussian Distributionshttps://scholarbank.nus.edu.sg/handle/10635/229646Title: High Dimensional Elliptical Sliced Inverse Regression in non-Gaussian Distributions
Authors: Xin Chen; Jia Zhang; Wang Zhou
Tue, 04 May 2021 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/2296462021-05-04T00:00:00Z
- Nonparametric statistical inference for P(Xhttps://scholarbank.nus.edu.sg/handle/10635/114363Title: Nonparametric statistical inference for P(X
Authors: Guangming, P.; Xiping, W.; Wang, Z.
Abstract: Let X, Y and Z be three independent random variables from three different populations. The stress-strength model P(X < Y < Z), the volume under the three-class ROC surface, has extensive applications in various areas since it provides a global measure of differences between or among populations. In this paper, we suggest to make statistical inference for P(X < Y < Z) via two methods, the nonparametric normal approximation and the jackknife empirical likelihood, since the usual empirical likelihood method for U-statistics is too complicated to apply. The results of the simulation studies indicate that these two methods work promisingly compared to other existing methods. Some classical and real data sets were analyzed using these two proposed methods. Practically, for simplicity, the nonparametric normal approximation method should be preferred; for better statistical results, one is suggested to use the JEL method although it is more complex than the normal approximation one. © 2013, Indian Statistical Institute.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1143632013-01-01T00:00:00Z
- Nonparametric statistical inference for P(Xhttps://scholarbank.nus.edu.sg/handle/10635/114940Title: Nonparametric statistical inference for P(X
Authors: Guangming, P.; Xiping, W.; Wang, Z.
Abstract: Let X, Y and Z be three independent random variables from three different populations. The stress-strength model P(X < Y < Z), the volume under the three-class ROC surface, has extensive applications in various areas since it provides a global measure of differences between or among populations. In this paper, we suggest to make statistical inference for P(X < Y < Z) via two methods, the nonparametric normal approximation and the jackknife empirical likelihood, since the usual empirical likelihood method for U-statistics is too complicated to apply. The results of the simulation studies indicate that these two methods work promisingly compared to other existing methods. Some classical and real data sets were analyzed using these two proposed methods. Practically, for simplicity, the nonparametric normal approximation method should be preferred; for better statistical results, one is suggested to use the JEL method although it is more complex than the normal approximation one. © 2013, Indian Statistical Institute.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1149402013-01-01T00:00:00Z
- Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matriceshttps://scholarbank.nus.edu.sg/handle/10635/127363Title: Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices
Authors: Bao, Z.; Pan, G.; Zhou, W.
Thu, 01 Jan 2015 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1273632015-01-01T00:00:00Z
- Factor Modelling for Clustering High-dimensional Time Serieshttps://scholarbank.nus.edu.sg/handle/10635/249184Title: Factor Modelling for Clustering High-dimensional Time Series
Authors: Bo Zhang; Guangming Pan; Qiwei Yao; Wang Zhou
Wed, 05 Apr 2023 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/2491842023-04-05T00:00:00Z