Sparse additive regression on a regular lattice

• 成果类型: Article
• 署名作者: Abramovich, Felix; Lahav, Tal
• 署名单位: Tel Aviv University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12075
• 发表日期: 2015
• 页码: 443-459
• 关键词: bayesian testimation; Optimal Rates; selection

摘要

We consider estimation in a sparse additive regression model with the design points on a regular lattice. We establish the minimax convergence rates over Sobolev classes and propose a Fourier-based rate optimal estimator which is adaptive to the unknown sparsity and smoothness of the response function. The estimator is derived within a Bayesian formalism but can be naturally viewed as a penalized maximum likelihood estimator with the complexity penalties on the number of non-zero univariate additive components of the response and on the numbers of the non-zero coefficients of their Fourer expansions. We compare it with several existing counterparts and perform a short simulation study to demonstrate its performance.