Abstract
In this paper, we consider the problem of simultaneous variable selection and estimation for varying-coefficient partially linear models in a “small \(n\), large \(p\)” setting, when the number of coefficients in the linear part diverges with sample size while the number of varying coefficients is fixed. Similar problem has been considered in Lam and Fan (Ann Stat 36(5):2232–2260, 2008) based on kernel estimates for the nonparametric part, in which no variable selection was investigated besides that \(p\) was assume to be smaller than \(n\). Here we use polynomial spline to approximate the nonparametric coefficients which is more computationally expedient, demonstrate the convergence rates as well as asymptotic normality of the linear coefficients, and further present the oracle property of the SCAD-penalized estimator which works for \(p\) almost as large as \(\exp \{n^{1/2}\}\) under mild assumptions. Monte Carlo studies and real data analysis are presented to demonstrate the finite sample behavior of the proposed estimator. Our theoretical and empirical investigations are actually carried out for the generalized varying-coefficient partially linear models, including both Gaussian data and binary data as special cases.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.