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期刊论文

Empirical likelihood condence regions in a partially linear single-index model

薛留根Lixing Zhu Liugen Xue

J. R. Statist. Soc. B (2006) 68, Part 3, pp.549-570,-0001,():

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摘要/描述

Empirical-likelihood-based inference for the parameters in a partially linear single- index model is investigated. Unlike existing empirical likelihood procedures for other simpler models; if there is no bias correction the limit distribution of the empirical likelihood ratio can- not be asymptotically tractable. To attack this difculty we propose a bias correction to achieve the standard χ2 -limit. The bias-corrected empirical likelihood ratio shares some of the desired features of the existing least squares method: the estimation of the parameters is not p needed; when estimating nonparametric functions in the model; undersmoothing for ensuring n-con- sistency of the estimator of the parameters is avoided; the bias-corrected empirical likelihood is self-scale invariant and no plug-in estimator for the limiting variance is needed. Furthermore; since the index is of norm 1; we use this constraint as information to increase the accuracy of the condence regions (smaller regions at the same nominal level). As a by-product; our approach of using bias correction may also shed light on nonparametric estimation in model checking for other semiparametric regression models. A simulation study is carried out to assess the performance of the bias-corrected empirical likelihood. An application to a real data set is illustrated.

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