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Sparse additive regression on a regular lattice
Author(s) -
Abramovich Felix,
Lahav Tal
Publication year - 2015
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12075
Subject(s) - minimax , univariate , estimator , mathematics , rate of convergence , sobolev space , minimax estimator , additive model , regression , algorithm , mathematical optimization , statistics , multivariate statistics , computer science , minimum variance unbiased estimator , mathematical analysis , computer network , channel (broadcasting)
Summary 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.