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Sparse additive regression on a regular lattice

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  • Felix Abramovich
  • Tal Lahav

Abstract

type="main" xml:id="rssb12075-abs-0001"> 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.

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  • Felix Abramovich & Tal Lahav, 2015. "Sparse additive regression on a regular lattice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 443-459, March.
    • Handle: RePEc:bla:jorssb:v:77:y:2015:i:2:p:443-459
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    File URL: http://hdl.handle.net/10.1111/rssb.2015.77.issue-2
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    Cited by:

    1. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    2. repec:esx:essedp:767 is not listed on IDEAS
    3. Gupta, A, 2015. "Autoregressive Spatial Spectral Estimates," Economics Discussion Papers 14458, University of Essex, Department of Economics.

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