Adaptive confidence region for the direction in semiparametric regressions |
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Authors: | Gao-Rong Li Li-Xing Zhu |
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Institution: | a College of Applied Sciences, Beijing University of Technology, Beijing, China b School of Finance and Statistics, East China Normal University, Shanghai, China c Department of Mathematics, Hong Kong Baptist University, Hong Kong, China |
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Abstract: | In this paper we aim to construct adaptive confidence region for the direction of ξ in semiparametric models of the form Y=G(ξTX,ε) where G(⋅) is an unknown link function, ε is an independent error, and ξ is a pn×1 vector. To recover the direction of ξ, we first propose an inverse regression approach regardless of the link function G(⋅); to construct a data-driven confidence region for the direction of ξ, we implement the empirical likelihood method. Unlike many existing literature, we need not estimate the link function G(⋅) or its derivative. When pn remains fixed, the empirical likelihood ratio without bias correlation can be asymptotically standard chi-square. Moreover, the asymptotic normality of the empirical likelihood ratio holds true even when the dimension pn follows the rate of pn=o(n1/4) where n is the sample size. Simulation studies are carried out to assess the performance of our proposal, and a real data set is analyzed for further illustration. |
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Keywords: | primary 62J05 secondary 62J07 |
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