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June 2015 Sparse high-dimensional varying coefficient model: Nonasymptotic minimax study
Olga Klopp, Marianna Pensky
Ann. Statist. 43(3): 1273-1299 (June 2015). DOI: 10.1214/15-AOS1309

Abstract

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.

Citation

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Olga Klopp. Marianna Pensky. "Sparse high-dimensional varying coefficient model: Nonasymptotic minimax study." Ann. Statist. 43 (3) 1273 - 1299, June 2015. https://doi.org/10.1214/15-AOS1309

Information

Received: 1 May 2014; Revised: 1 January 2015; Published: June 2015
First available in Project Euclid: 15 May 2015

zbMATH: 1328.62339
MathSciNet: MR3346703
Digital Object Identifier: 10.1214/15-AOS1309

Subjects:
Primary: 62H12, 62J05
Secondary: 62C20

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 3 • June 2015
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