Sparse additive regression on a regular lattice

Felix Abramovich, Tal Lahav

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)443-459
Number of pages17
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume77
Issue number2
DOIs
StatePublished - 1 Mar 2015

Keywords

  • Adaptive minimaxity
  • Additive models
  • Complexity penalty
  • Maximum a posteriori rule
  • Sparsity

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