ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 03 Feb 2023 11:32:43 GMT2023-02-03T11:32:43Z50161- Some asymptotic results on Box-Cox transformation methodologyhttps://scholarbank.nus.edu.sg/handle/10635/19367Title: Some asymptotic results on Box-Cox transformation methodology
Authors: Yang, Z.
Mon, 01 Jan 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/193671996-01-01T00:00:00Z
- More on the estimation of Box-Cox transformationhttps://scholarbank.nus.edu.sg/handle/10635/19392Title: More on the estimation of Box-Cox transformation
Authors: Yang, Z.
Wed, 01 Jan 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/193921997-01-01T00:00:00Z
- More on the MIS-specification of the shape parameter with Weibull-to-exponential transformationhttps://scholarbank.nus.edu.sg/handle/10635/51860Title: More on the MIS-specification of the shape parameter with Weibull-to-exponential transformation
Authors: Xie, M.; Yang, Z.; Gaudoin, O.
Abstract: When lifetimes follow Weibull distribution with known shape parameter, a simple power transformation could be used to transform the data to the case of exponential distribution, which is much easier to analyze. Usually, the shape parameter cannot be known exactly and it is important to investigate the effect of mis-specification of this parameter. In a recent article, it was suggested that the Weibull-to-exponential transformation approach should not be used as the confidence interval for the scale parameter has very poor statistical property. However, it would be of interest to study the use of Weibull-to-exponential transformation when the mean time to failure or reliability is to be estimated, which is a more common question. In this paper, the effect of mis-specification of Weibull shape parameters on these quantities is investigated. For reliability-related quantities such as mean time to failure, percentile lifetime and mission reliability, the Weibull-to-exponential transformation approach is generally acceptable. For the cases when the data are highly censored or when small tail probability is concerned, further studies are needed, but these are known to be difficult statistical problems for which there are no standard solutions.
Sat, 01 Jul 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/518602000-07-01T00:00:00Z
- An explicit variance formula for the Box-Cox functional form estimatorhttps://scholarbank.nus.edu.sg/handle/10635/19971Title: An explicit variance formula for the Box-Cox functional form estimator
Authors: Yang, Z.; Abeysinghe, T.
Abstract: Although the Box-Cox transformation provides a flexible functional form for regression models, its applicability is often hampered by the difficulty of choosing an appropriate value for the Box-Cox parameter. This paper presents an explicit variance formula for the Box-Cox estimator of the functional form, from which the analytical behavior of the estimator and its precision can be assessed.©2002 Elsevier Science B.V. All rights reserved.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/199712002-01-01T00:00:00Z
- A comparison of likelihood and Bayesian inference for the threshold parameter in the inverse Gaussian distributionhttps://scholarbank.nus.edu.sg/handle/10635/105490Title: A comparison of likelihood and Bayesian inference for the threshold parameter in the inverse Gaussian distribution
Authors: Desmond, A.F.; Yang, Z.
Abstract: Likelihood and Bayesian inferences for the threshold parameter of the three parameter inverse Gaussian distribution are compared and contrasted. When there is no prior information available and sample size is moderate, theoretical and empirical results suggest advantages to the Bayesian approach. Use of the conjugate prior can favorably affect the Bayesian inference in a substantial way. Copyright © 1998 by Marcel Dekker, Inc.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1054901998-01-01T00:00:00Z
- Predictive densities for the lognormal distribution and their applicationshttps://scholarbank.nus.edu.sg/handle/10635/105305Title: Predictive densities for the lognormal distribution and their applications
Authors: Yang, Z.
Abstract: Maximum likelihood predictive densities (MLPDs) for a future lognormal observation are obtained and their applications to reliability and life testing are considered. When applied to reliability and failure rate estimations, they give estimators that can be much less biased and less variable than the usual maximum likelihood estimations (MLEs) obtained by replacing the unknown parameters in the density function by their MLEs. When applied to lifetime predictions, they give prediction intervals that are shorter than the usual frequentist intervals. Using the MLPDs, it is also rather convenient to construct the shortest prediction intervals. Extensive simulations are performed for comparisons. A numerical example is given for illustration. © 2000 Elsevier Science Ltd. All rights reserved.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1053051999-01-01T00:00:00Z
- On the failure rate estimation of the inverse Gaussian distributionhttps://scholarbank.nus.edu.sg/handle/10635/105272Title: On the failure rate estimation of the inverse Gaussian distribution
Authors: Yang, Z.; Lee, R.T.C.
Abstract: New estimators of the inverse Gaussian failure rate are proposed based on the maximum likelihood predictive densities derived by Yang (1999). These estimators are compared, via Monte Carlo simulation, with the usual maximum likelihood estimators of the failure rate and found to be superior in terms of bias and mean squared error. Sensitivity of the estimators against the departure from the inverse Gaussian distribution is studied.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052722001-01-01T00:00:00Z
- On robustness of usual confidence region under transformation misspecificationhttps://scholarbank.nus.edu.sg/handle/10635/105264Title: On robustness of usual confidence region under transformation misspecification
Authors: Yang, Z.
Abstract: Robustness of confidence region for linear model parameters following a misspecified transformation of dependent variable is studied. It is shown that when error standard deviation is moderate to large the usual confidence region is robust against transformation misspecification. When error standard deviation is small the usual confidence region could be very conservative for structured models and slightly liberal for unstructured models. However, the conservativeness in structured case can be controlled if the transformation is selected with the help of data rather than prior information since this is the case when data is able to provide a very accurate estimate of transformation.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052641998-01-01T00:00:00Z
- A new statistic for regression transformationhttps://scholarbank.nus.edu.sg/handle/10635/104948Title: A new statistic for regression transformation
Authors: Yang, Z.
Abstract: A new statistic for testing a regression transformation is proposed based on a result of Yang (1999). This statistic is shown to be stable, having a null distribution almost independent of model type and parameter values, accurate and easy to implement. The statistic is of the Wald-type and thus is compared with the Wald statistic given by Lawrance (1987) in terms of size, null distribution and power using simulation. The simulation results show that the new statistic generally outperforms that of Lawrance.
Thu, 01 Jun 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1049482000-06-01T00:00:00Z
- An alternative approximation to the variance of transformation scorehttps://scholarbank.nus.edu.sg/handle/10635/104991Title: An alternative approximation to the variance of transformation score
Authors: Yang, Z.
Abstract: An alternative approximation to the variance of transformation score is given, based on an asymptotic expansion of the transformation estimator. It is then compared with the variance approximation given by Lawrance (1987) in terms of standardized scores. Simulations show that the two standardized scores behave very similarly when model error standard deviation is small. However, when error standard deviation is not small, the new standardized score outperforms that of Lawrance, especially in the structured models.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1049911998-01-01T00:00:00Z
- Predicting a Future Median Life through a Power Transformationhttps://scholarbank.nus.edu.sg/handle/10635/105304Title: Predicting a Future Median Life through a Power Transformation
Authors: Yang, Z.
Abstract: A simple and unified prediction interval (PI) for the median of a future lifetime can be obtained through a power transformation. This interval usually possesses the correct coverage, at least asymptotically, when the transformation is known. However, when the transformation is unknown and is estimated from the data, a correction is required. A simple correction factor is derived based on large sample theory. Simulation shows that the unified PI after correction performs well. When compared with the existing frequentist PI's, it shows an equivalent or a better performance in terms of coverage probability and average length of the interval. Its nonparametric aspect and the ease of usage make it very attractive to practitioners. Real data examples are provided for illustration.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1053042001-01-01T00:00:00Z
- Maximum likelihood predictive densities for the inverse Gaussian distribution with applications to reliability and lifetime predictionshttps://scholarbank.nus.edu.sg/handle/10635/105215Title: Maximum likelihood predictive densities for the inverse Gaussian distribution with applications to reliability and lifetime predictions
Authors: Yang, Z.
Abstract: Maximum likelihood predictive densities (MLPD) for the inverse Gaussian distribution are derived for the cases of one or both parameters unknown. They are then applied to obtain estimators of the reliability function and prediction or shortest prediction intervals for a future observation. Comparisons with the existing likelihood or frequentist methods show that the MLPD estimators of reliability gives smaller bias and smaller MSE for a wide range of population values, and that the MLPD prediction intervals are shorter while preserving the correct coverage probability. The shortest MLPD prediction intervals further sharpen the above equitailed MLPD intervals in terms of interval lengths.
Wed, 01 Sep 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1052151999-09-01T00:00:00Z
- An investigation of transformation-based prediction interval for the Weibull median lifehttps://scholarbank.nus.edu.sg/handle/10635/51853Title: An investigation of transformation-based prediction interval for the Weibull median life
Authors: Yang, Z.; See, S.P.; Xie, M.
Abstract: Statistical inference based on the Weibull distribution, a distribution widely used in reliability and survival analysis, is usually difficult as it often involves numerical computation and approximation. However, this distribution can be transformed to near-normality by a simple power transformation. Based on this transformation, a prediction interval (PI) for its median can be easily constructed through an inverse transformation. The procedure for selecting the best power transformation through minimizing Kullback-Leibler information is described. The property of this transformation-based PI is investigated. Simple correction factors are also proposed. It is shown that the transformation-based PI with corrections performs well, irrespective of the sample size and parameter values. Simulation results show that the new PI generally outperforms the existing PI. Numerical examples are given for illustration.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/518532002-01-01T00:00:00Z
- An explicit variance formula for the Box-Cox functional form estimatorhttps://scholarbank.nus.edu.sg/handle/10635/104997Title: An explicit variance formula for the Box-Cox functional form estimator
Authors: Yang, Z.; Abeysinghe, T.
Abstract: Although the Box-Cox transformation provides a flexible functional form for regression models, its applicability is often hampered by the difficulty of choosing an appropriate value for the Box-Cox parameter. This paper presents an explicit variance formula for the Box-Cox estimator of the functional form, from which the analytical behavior of the estimator and its precision can be assessed. © 2002 Elsevier Science B.V. All rights reserved.
Mon, 01 Jul 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1049972002-07-01T00:00:00Z
- Transformation approaches for the construction of Weibull prediction intervalhttps://scholarbank.nus.edu.sg/handle/10635/63384Title: Transformation approaches for the construction of Weibull prediction interval
Authors: Yang, Z.; See, S.P.; Xie, M.
Abstract: Two methods of transforming the Weibull data to near normality, namely the Box-Cox method and Kullback-Leibler (KL) information method, are discussed and contrasted. A simple prediction interval (PI) based on the better KL information method is proposed. The asymptotic property of this interval is established. Its small sample behavior is investigated using Monte Carlo simulation. Simulation results show that this simple interval is close to the existing complicated PI where the percentage points of the reference distribution have to be either simulated or approximated. The proposed interval can also be easily adjusted to have the correct asymptotic coverage. © 2002 Elsevier Science B.V. All rights reserved.
Mon, 28 Jul 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/633842003-07-28T00:00:00Z
- Predicting a Future Lifetime through Box-Cox Transformationhttps://scholarbank.nus.edu.sg/handle/10635/105303Title: Predicting a Future Lifetime through Box-Cox Transformation
Authors: Yang, Z.
Abstract: In predicting a future lifetime based on a sample of past lifetimes, the Box-Cox transformation method provides a simple and unified procedure that is shown in this article to meet or often outperform the corresponding frequentist solution in terms of coverage probability and average length of prediction intervals. Kullback-Leibler information and second-order asymptotic expansion are used to justify the Box-Cox procedure. Extensive Monte Carlo simulations are also performed to evaluate the small sample behavior of the procedure. Certain popular lifetime distributions, such as Weibull, inverse Gaussian and Birnbaum-Saunders are served as illustrative examples. One important advantage of the Box-Cox procedure lies in its easy extension to linear model predictions where the exact frequentist solutions are often not available.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1053031999-01-01T00:00:00Z