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May 2021 Minimax predictive density for sparse count data
Keisuke Yano, Ryoya Kaneko, Fumiyasu Komaki
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Bernoulli 27(2): 1212-1238 (May 2021). DOI: 10.3150/20-BEJ1271


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.


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Keisuke Yano. Ryoya Kaneko. Fumiyasu Komaki. "Minimax predictive density for sparse count data." Bernoulli 27 (2) 1212 - 1238, May 2021.


Received: 1 November 2019; Revised: 1 June 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.3150/20-BEJ1271

Keywords: Adaptation , high dimension , Kullback–Leibler divergence , missing at random , Poisson model , Zero inflation

Rights: Copyright © 2021 ISI/BS


Vol.27 • No. 2 • May 2021
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