Authors: Zhu, Lixing¹; Xue, Liugen²

Source: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 68, Number 3, June 2006 , pp. 549-570(22)

Publisher: Wiley-Blackwell

Abstract:

Summary. 

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 cannot be asymptotically tractable. To attack this difficulty 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 needed; when estimating nonparametric functions in the model, undersmoothing for ensuring √n-consistency 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 confidence 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.

Keywords: Confidence region; Coverage probability; χ2-distribution; Empirical likelihood; Partially linear single-index models

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2006.00556.x

Affiliations: 1: Hong Kong Baptist University and Renmin University of China, Beijing, People's Republic of China 2: Beijing University of Technology, People's Republic of China

Publication date: 2006-06-01

Related content

• In this: publication
• By this: publisher
• In this Subject: Mathematics and Statistics
• By this author: Zhu, Lixing ;  Xue, Liugen

Website © Publishing Technology. Article copyright remains with the publisher, society or author(s) as specified within the article.

• Terms and conditions
• Privacy policy
• Information for advertisers