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Empirical likelihood for the varying‐coefficient single‐index model
Authors:Zhensheng Huang  Riquan Zhang
Affiliation:1. School of Mathematics, Hefei University of Technology, Hefei, 230009, People's Republic of China;2. Department of Statistics, East China Normal University, Shanghai, 200241, People's Republic of China;3. Department of Mathematics, Shanxi Datong University, Datong, Shanxi, 037009, People's Republic of China
Abstract:In this article the author investigates the application of the empirical‐likelihood‐based inference for the parameters of varying‐coefficient single‐index model (VCSIM). Unlike the usual cases, if there is no bias correction the asymptotic distribution of the empirical likelihood ratio cannot achieve the standard chi‐squared distribution. To this end, a bias‐corrected empirical likelihood method is employed to construct the confidence regions (intervals) of regression parameters, which have two advantages, compared with those based on normal approximation, that is, (1) they do not impose prior constraints on the shape of the regions; (2) they do not require the construction of a pivotal quantity and the regions are range preserving and transformation respecting. A simulation study is undertaken to compare the empirical likelihood with the normal approximation in terms of coverage accuracies and average areas/lengths of confidence regions/intervals. A real data example is given to illustrate the proposed approach. The Canadian Journal of Statistics 38: 434–452; 2010 © 2010 Statistical Society of Canada
Keywords:Confidence region  chi‐squared distribution  empirical likelihood  stepwise method  varying‐coefficient single‐index model. MSC 2000 Primary 62G08  secondary 62E20.
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