Spline estimator for ultra-high dimensional partially linear varying coefficient models

Zhaoliang Wang (), Liugen Xue, Gaorong Li and Fei Lu
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Zhaoliang Wang: Beijing University of Technology
Liugen Xue: Beijing University of Technology
Gaorong Li: Beijing University of Technology
Fei Lu: Beijing University of Technology

Annals of the Institute of Statistical Mathematics, 2019, vol. 71, issue 3, No 8, 657-677

Abstract: Abstract In this paper, we simultaneously study variable selection and estimation problems for sparse ultra-high dimensional partially linear varying coefficient models, where the number of variables in linear part can grow much faster than the sample size while many coefficients are zeros and the dimension of nonparametric part is fixed. We apply the B-spline basis to approximate each coefficient function. First, we demonstrate the convergence rates as well as asymptotic normality of the linear coefficients for the oracle estimator when the nonzero components are known in advance. Then, we propose a nonconvex penalized estimator and derive its oracle property under mild conditions. Furthermore, we address issues of numerical implementation and of data adaptive choice of the tuning parameters. Some Monte Carlo simulations and an application to a breast cancer data set are provided to corroborate our theoretical findings in finite samples.

Keywords: High dimensionality; Partially linear varying coefficient model; Variable selection; Nonconvex penalty; Oracle property (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10463-018-0654-0

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