Semi-varying coefficient models with a diverging number of components

Gaorong Li, Liugen Xue and Heng Lian

Journal of Multivariate Analysis, 2011, vol. 102, issue 7, 1166-1174

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.

Keywords: B-spline; basis; Diverging; parameters; Semi-varying; coefficient; models (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (8)

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