an:05915061
Zbl 1216.62060
Li, Gaorong; Xue, Liugen; Lian, Heng
Semi-varying coefficient models with a diverging number of components
EN
J. Multivariate Anal. 102, No. 7, 1166-1174 (2011).
00281674
2011
j
62G08 62G20 65C05 65D07
\(B\)-spline basis; diverging parameters
Summary: 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. 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.