Semi-varying coefficient models with a diverging number of components |
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Authors: | Gaorong LiLiugen Xue Heng Lian |
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Affiliation: | a College of Applied Sciences, Beijing University of Technology, Beijing 100124, Chinab Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore |
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Abstract: | Semiparametric models with both nonparametric and parametric components have become increasingly useful in many scientific fields, due to their appropriate representation of the trade-off between flexibility and efficiency of statistical models. In this paper we focus on semi-varying coefficient models (a.k.a. varying coefficient partially linear models) in a “large n, diverging p” situation, when both the number of parametric and nonparametric components diverges at appropriate rates, and we only consider the case p=o(n). Consistency of the estimator based on B-splines and asymptotic normality of the linear components are established under suitable assumptions. Interestingly (although not surprisingly) our analysis shows that the number of parametric components can diverge at a faster rate than the number of nonparametric components and the divergence rates of the number of the nonparametric components constrain the allowable divergence rates of the parametric components, which is a new phenomenon not established in the existing literature as far as we know. Finally, the finite sample behavior of the estimator is evaluated by some Monte Carlo studies. |
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Keywords: | 62G08 62G20 |
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