Bias-corrected empirical likelihood in a multi-link semiparametric model

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Zhu, Lixing^2,5  Lin, Lu¹  Cui, Xia^1,4  Li, Gaorong³ 

[1] Shandong Univ, Sch Math & Syst Sci, Jinan 250100, Peoples R China

[2] Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China

[3] Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

[4] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

[5] Yunnan Univ Finance & Econ, Sch Math & Stat, Kunming 650221, Peoples R China

关键词: Empirical likelihood ratio;    Bias correction;    Multi-link semiparametric model;    Confidence region;    Test statistic;    Chi-square distribution;   

DOI  :  10.1016/j.jmva.2009.08.009

来源: Elsevier

【 摘 要 】

In this paper, we investigate the empirical likelihood for constructing a confidence region of the parameter of interest in a multi-link semiparametric model when an infinite-dimensional nuisance parameter exists. The new model covers the commonly used varying coefficient, generalized linear, single-index, multi-index, hazard regression models and their generalizations, as its special cases. Because of the existence of the infinite-dimensional nuisance parameter, the classical empirical likelihood with plug-in estimation cannot be asymptotically distribution-free, and the existing bias correction is not extendable to handle Such a general model. We then propose a link-based correction approach to solve this problem. This approach gives a general rule of bias correction via an inner link, and consists of two parts. For the model whose estimating equation contains the score functions that are easy to estimate, we use a centering for the scores to correct the bias; for the model of which the score functions are of complex structure, a bias-correction procedure using simpler functions instead of the scores is given without loss of asymptotic efficiency. The resulting empirical likelihood shares the desired features: it has a chi-square limit and, under-smoothing technique, high order kernel and parameter estimation are not needed. Simulation studies are carried out to examine the performance of the new method. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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