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2017 Asymptotically minimax prediction in infinite sequence models
Keisuke Yano, Fumiyasu Komaki
Electron. J. Statist. 11(2): 3165-3195 (2017). DOI: 10.1214/17-EJS1312

Abstract

We study asymptotically minimax predictive distributions in infinite sequence models. First, we discuss the connection between prediction in an infinite sequence model and prediction in a function model. Second, we construct an asymptotically minimax predictive distribution for the setting in which the parameter space is a known ellipsoid. We show that the Bayesian predictive distribution based on the Gaussian prior distribution is asymptotically minimax in the ellipsoid. Third, we construct an asymptotically minimax predictive distribution for any Sobolev ellipsoid. We show that the Bayesian predictive distribution based on the product of Stein’s priors is asymptotically minimax for any Sobolev ellipsoid. Finally, we present an efficient sampling method from the proposed Bayesian predictive distribution.

Citation

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Keisuke Yano. Fumiyasu Komaki. "Asymptotically minimax prediction in infinite sequence models." Electron. J. Statist. 11 (2) 3165 - 3195, 2017. https://doi.org/10.1214/17-EJS1312

Information

Received: 1 June 2016; Published: 2017
First available in Project Euclid: 11 September 2017

zbMATH: 1373.62039
MathSciNet: MR3697133
Digital Object Identifier: 10.1214/17-EJS1312

Subjects:
Primary: 62C20, 62G20
Secondary: 62C10

JOURNAL ARTICLE
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Vol.11 • No. 2 • 2017
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