Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters

JOURNAL OF MULTIVARIATE ANALYSIS

卷:105

Article

Li, Gaorong¹  Lin, Lu²  Zhu, Lixing^3,4 

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

[2] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

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

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

关键词: Varying coefficient partially linear model;    Empirical likelihood;    Bias correction;    Asymptotic normality;    Curse of dimensionality;   

DOI  :  10.1016/j.jmva.2011.08.010

来源: Elsevier

【 摘 要 】

The purpose of this paper is two-fold. First, for the estimation or inference about the parameters of interest in semiparametric models, the commonly used plug-in estimation for infinite-dimensional nuisance parameter creates non-negligible bias, and the least favorable curve or under-smoothing is popularly employed for bias reduction in the literature. To avoid such strong structure assumptions on the models and inconvenience of estimation implementation, for the diverging number of parameters in a varying coefficient partially linear model, we adopt a bias-corrected empirical likelihood (BCEL) in this paper. This method results in the distribution of the empirical likelihood ratio to be asymptotically tractable. It can then be directly applied to construct confidence region for the parameters of interest. Second, different from all existing methods that impose strong conditions to ensure consistency of estimation when diverging the number of the parameters goes to infinity as the sample size goes to infinity, we provide techniques to show that, other than the usual regularity conditions, the consistency holds under moment conditions alone on the covariates and error with a diverging rate being even faster than those in the literature. A simulation study is carried out to assess the performance of the proposed method and to compare it with the profile least squares method. A real dataset is analyzed for illustration. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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