Inference on varying-coefficient partially linear regression model

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• 作者：Jing-yan Feng ; Ri-quan Zhang ; Yi-qiang Lu
• 关键词：asymptotic normality ; varying ; coefficient partially linear regression model ; generalized likelihood ratio test ; Wilks phenomenon ; χ2 ; distribution ; 62G10 ; 62G12
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：31
• 期：1
• 页码：139-156
• 全文大小：521 KB
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• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. (2008) proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized likelihood ratio test is established. Under the null hypotheses the normalized test statistic follows a χ2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance parameters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.