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.
|Number of pages||17|
|Journal||Journal of the Royal Statistical Society. Series B: Statistical Methodology|
|State||Published - 1 Mar 2015|
- Adaptive minimaxity
- Additive models
- Complexity penalty
- Maximum a posteriori rule