SPARSE HIGH-DIMENSIONAL VARYING COEFFICIENT MODEL: NONASYMPTOTIC MINIMAX STUDY

• 成果类型: Article
• 署名作者: Klopp, Olga; Pensky, Marianna
• 署名单位: Universite Paris Saclay; State University System of Florida; University of Central Florida
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1309
• 发表日期: 2015
• 页码: 1273-1299
• 关键词: oracle inequalities; spline estimation; group lasso; inference

摘要

The objective of the present paper is to develop a minimax theory for the varying coefficient model in a nonasymptotic setting. We consider a high-dimensional sparse varying coefficient model where only few of the covariates are present and only some of those covariates are time dependent. Our analysis allows the time-dependent covariates to have different degrees of smoothness and to be spatially inhomogeneous. We develop the minimax lower bounds for the quadratic risk and construct an adaptive estimator which attains those lower bounds within a constant (if all time-dependent covariates are spatially homogeneous) or logarithmic factor of the number of observations.