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October 2019 Projected spline estimation of the nonparametric function in high-dimensional partially linear models for massive data
Heng Lian, Kaifeng Zhao, Shaogao Lv
Ann. Statist. 47(5): 2922-2949 (October 2019). DOI: 10.1214/18-AOS1769

Abstract

In this paper, we consider the local asymptotics of the nonparametric function in a partially linear model, within the framework of the divide-and-conquer estimation. Unlike the fixed-dimensional setting in which the parametric part does not affect the nonparametric part, the high-dimensional setting makes the issue more complicated. In particular, when a sparsity-inducing penalty such as lasso is used to make the estimation of the linear part feasible, the bias introduced will propagate to the nonparametric part. We propose a novel approach for estimation of the nonparametric function and establish the local asymptotics of the estimator. The result is useful for massive data with possibly different linear coefficients in each subpopulation but common nonparametric function. Some numerical illustrations are also presented.

Citation

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Heng Lian. Kaifeng Zhao. Shaogao Lv. "Projected spline estimation of the nonparametric function in high-dimensional partially linear models for massive data." Ann. Statist. 47 (5) 2922 - 2949, October 2019. https://doi.org/10.1214/18-AOS1769

Information

Received: 1 April 2018; Revised: 1 July 2018; Published: October 2019
First available in Project Euclid: 3 August 2019

zbMATH: 07114933
MathSciNet: MR3988777
Digital Object Identifier: 10.1214/18-AOS1769

Subjects:
Primary: 62G08
Secondary: 62G20

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 5 • October 2019
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