Empirical Likelihood Inference for the Parameter in Additive Partially Linear EV Models |
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Authors: | Xiuli Wang Fang Chen Lu Lin |
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Institution: | 1. School of Mathematics , Shandong University , Jinan, P.R. China;2. School of Mathematical Science , Shandong Normal University , Jinan, P.R. China xiuliwang168@sina.com.cn;4. Department of Basic Sciences , Guangzhou Nanyang College , Guangzhou, P.R. China;5. School of Mathematics , Shandong University , Jinan, P.R. China |
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Abstract: | In this article, we consider empirical likelihood inference for the parameter in the additive partially linear models when the linear covariate is measured with error. By correcting for attenuation, a corrected-attenuation empirical log-likelihood ratio statistic for the unknown parameter β, which is of primary interest, is suggested. We show that the proposed statistic is asymptotically standard chi-square distribution without requiring the undersmoothing of the nonparametric components, and hence it can be directly used to construct the confidence region for the parameter β. Some simulations indicate that, in terms of comparison between coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the profile-based least-squares method. We also give the maximum empirical likelihood estimator (MELE) for the unknown parameter β, and prove the MELE is asymptotically normal under some mild conditions. |
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Keywords: | Additive model Confidence regions Empirical likelihood Errors-in-variables Partially linear regression model |
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