Abstract
One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically χ 2-distribution and theWilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.
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This research was supported by National Natural Science Foundation of China under Grant No. 1117112, the Fund of Shanxi Datong University under Grant No. 2010K4, the Doctoral Fund of Ministry of Education of China under Grant No. 20090076110001, and National Statistical Science Research Major Program of China under Grant No. 2011LZ051.
This paper was recommended for publication by Editor Guohua ZOU.
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Feng, J., Zhang, R. Inference on coefficient function for varying-coefficient partially linear model. J Syst Sci Complex 25, 1143–1157 (2012). https://doi.org/10.1007/s11424-012-0324-x
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DOI: https://doi.org/10.1007/s11424-012-0324-x