Empirical likelihood ratio tests for multivariate regression models

WU Jianhong; ZHU Lixing

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Empirical likelihood ratio tests for multivariate regression models

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This paper proposes some diagnostic tools for checking the adequacy of multivariate regression models including classical regression and time series autoregression. In statistical inference, the empirical likelihood ratio method has been well known to be a powerful tool for constructing test and confidence region. For model checking, however, the naive empirical likelihood (EL) based tests are not of Wilks' phenomenon. Hence, we make use of bias correction to construct the EL-based score tests and derive a nonparametric version of Wilks' theorem. Moreover, by the advantages of both the EL and score test method, the EL-based score tests share many desirable features as follows: They are self-scale invariant and can detect the alternatives that converge to the null at rate n-1/2, the possibly fastest rate for lack-of-fit testing; they involve weight functions, which provides us with the flexibility to choose scores for improving power performance, especially under directional alternatives. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of possible alternatives. A simulation study is carried out and an application for a real dataset is analyzed.

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来源
《中国高等学校学术文摘·数学》 |2007年第1期|149-168|共20页
作者
WU Jianhong; ZHU Lixing;
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作者单位

Department of Statistics, East China Normal University, Shanghai 200062,China;

College of Statistics & Computing Science, Zhejiang Congshang University, Hangzhou 310018, China;

Department of Statistics, East China Normal University, Shanghai 200062,China;

Department of Mathematics, Hong Kong Baptist University, Hong Kong, China;

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原文格式 PDF
正文语种 chi
中图分类数学;
关键词
autoregression; bias correction; empirical likelihood ratio test; maximin test; multivariate regression;

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Empirical likelihood ratio tests for multivariate regression models

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