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We consider estimation in a sparse additive regression model with the designpoints on a regular lattice. We establish the minimax convergence rates overSobolev classes and propose a Fourier-based rate-optimal estimator which isadaptive to the unknown sparsity and smoothness of the response function. Theestimator is derived within Bayesian formalism but can be naturally viewed as apenalized maximum likelihood estimator with the complexity penalties on thenumber of nonzero univariate additive components of the response and on thenumbers of the nonzero coefficients of their Fourer expansions. We compare itwith several existing counterparts and perform a short simulation study todemonstrate its performance.

Sparse additive regression on a regular lattice