Minimax Predictive Density for Sparse Count Data

Abstract

This paper discusses predictive densities under the Kullback--Leibler loss for high-dimensional Poisson sequence models under sparsity constraints. Sparsity in count data implies zero-inflation. We present a class of Bayes predictive densities that attain asymptotic minimaxity in sparse Poisson sequence models. We also show that our class with an estimator of unknown sparsity level plugged-in is adaptive in the asymptotically minimax sense. For application, we extend our results to settings with quasi-sparsity and with missing-completely-at-random observations. The simulation studies as well as application to real data illustrate the efficiency of the proposed Bayes predictive densities.

49 pages; the supplement is included in pp. 32-49 Accepted for publication in Bernoulli journal

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Cited by in corpus (1)

• On Global-local Shrinkage Priors for Count Data