Empirical likelihood inferences for varying coefficient partially nonlinear models |
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Authors: | Xiaoshuang Zhou Peixin Zhao Xiuli Wang |
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Institution: | 1. School of Mathematical Sciences, Dezhou University, Dezhou, Shandong, People's Republic of China;2. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, People's Republic of China;3. School of Mathematical Sciences, Shandong Normal University, Jinan, Shandong, People's Republic of China |
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Abstract: | In this article, empirical likelihood inferences for the varying coefficient partially nonlinear models are investigated. An empirical log-likelihood ratio function for the unknown parameter vector in the nonlinear function part and a residual-adjusted empirical log-likelihood ratio function for the nonparametric component are proposed. The corresponding Wilks phenomena are proved and the confidence regions for parametric component and nonparametric component are constructed. Simulation studies indicate that, in terms of coverage probabilities and average areas of the confidence regions, the empirical likelihood method performs better than the normal approximation-based method. Furthermore, a real data set application is also provided to illustrate the proposed empirical likelihood estimation technique. |
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Keywords: | Empirical likelihood varying coefficient partially nonlinear model profile nonlinearleast-squares estimation confidence region parameter vector |
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