Statistical inference on seemingly unrelated varying coefficient partially linear models |
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Authors: | Jinhong You Xian Zhou |
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Institution: | 1. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China;2. Department of Actuarial Studies, Macquarie University, North Ryde, Sydney, NSW 2109, Australia |
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Abstract: | This paper is concerned with the statistical inference on seemingly unrelated varying coefficient partially linear models. By combining the local polynomial and profile least squares techniques, and estimating the contemporaneous correlation, we propose a class of weighted profile least squares estimators (WPLSEs) for the parametric components. It is shown that the WPLSEs achieve the semiparametric efficiency bound and are asymptotically normal. For the non‐parametric components, by applying the undersmoothing technique, and taking the contemporaneous correlation into account, we propose an efficient local polynomial estimation. The resulting estimators are shown to have mean‐squared errors smaller than those estimators that neglect the contemporaneous correlation. In addition, a class of variable selection procedures is developed for simultaneously selecting significant variables and estimating unknown parameters, based on the non‐concave penalized and weighted profile least squares techniques. With a proper choice of regularization parameters and penalty functions, the proposed variable selection procedures perform as efficiently as if one knew the true submodels. The proposed methods are evaluated using wide simulation studies and applied to a set of real data. |
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Keywords: | semiparametric model seemingly unrelated partially linear varying coefficient primary 62G05 secondary 62G20 62M10 |
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