PROJECTED SPLINE ESTIMATION OF THE NONPARAMETRIC FUNCTION IN HIGH-DIMENSIONAL PARTIALLY LINEAR MODELS FOR MASSIVE DATA

• 成果类型: Article
• 署名作者: Lian, Heng; Zhao, Kaifeng; Lv, Shaogao
• 署名单位: City University of Hong Kong; Philips; Philips Research; Nanjing Audit University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1769
• 发表日期: 2019
• 页码: 2922-2949
• 关键词: efficient estimation; variable selection; local asymptotics; regression

摘要

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.