Empirical likelihood inference in partially linear single-index models for longitudinal data

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Li, Gaorong¹  Zhu, Lixing²  Xue, Liugen¹  Feng, Sanying³ 

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

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

[3] Luoyang Normal Univ, Coll Math & Sci, Luoyang 471022, Peoples R China

关键词: Longitudinal data;    Partially linear single-index model;    Empirical likelihood;    Confidence region;    Bias correction;   

DOI  :  10.1016/j.jmva.2009.08.006

来源: Elsevier

【 摘 要 】

The empirical likelihood method is especially useful for constructing confidence intervals or regions of parameters of interest. Yet, the technique cannot be directly applied to partially linear single-index models for longitudinal data due to the within-subject correlation. In this paper, a bias-corrected block empirical likelihood (BCBEL) method is suggested to study the models by accounting for the within-subject correlation. BCBEL shares some desired features: unlike any normal approximation based method for confidence region, the estimation of parameters with the iterative algorithm is avoided and a consistent estimator of the asymptotic covariance matrix is not needed. Because of bias correction, the BCBEL ratio is asymptotically chi-squared, and hence it can be directly used to construct confidence regions of the parameters without any extra Monte Carlo approximation that is needed when bias correction is not applied. The proposed method can naturally be applied to deal with pure single-index models and partially linear models for longitudinal data. Some simulation studies are carried out and an example in epidemiology is given for illustration. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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