Please use this identifier to cite or link to this item: https://doi.org/10.1080/10485250902980584
Title: Statistical inference for induced L-statistics: A random perturbation approach
Authors: Xu, J. 
Zhao, L.
Leng, C. 
Keywords: L-statistics
Order statistics
Random perturbation
Issue Date: Oct-2009
Citation: Xu, J., Zhao, L., Leng, C. (2009-10). Statistical inference for induced L-statistics: A random perturbation approach. Journal of Nonparametric Statistics 21 (7) : 863-876. ScholarBank@NUS Repository. https://doi.org/10.1080/10485250902980584
Abstract: Suppose that X and Y are two numerical characteristics defined for each individual in a population. In a random sample of (X,Y) with sample size n, denote the rth ordered X variate by Xr:n and the associated Y variate, the induced rth order statistics, by Y[r:n], respectively. Induced order statistics arise naturally in the context of selection where individuals ought to be selected by their ranks in a related X value due to difficulty or h∑gh costs of obtaining Y at the time of selection. The induced L-statistics, which take the form of, are very useful in regression analysis, especially when the observations are subject to a type-II censoring scheme with respect to the dependent variable, or when the regression function at a given quantile of the predictor variable is of interest. The limiting variance of the induced L-statistics involve the underlying regression function and inferences based on nonparametric estimation are often unstable. In this paper, we consider the distributional approximation of the induced L-statistics by the random perturbation method. Large sample properties of the randomly perturbed induced L-statistics are established. Numerical studies are also conducted to illustrate the method and to assess its finite-sample performance. © 2009 Taylor & Francis.
Source Title: Journal of Nonparametric Statistics
URI: http://scholarbank.nus.edu.sg/handle/10635/105390
ISSN: 10485252
DOI: 10.1080/10485250902980584
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