Electronic Journal of Statistics

Asymptotically minimax prediction in infinite sequence models

Keisuke Yano and Fumiyasu Komaki

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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.

Article information

Electron. J. Statist. Volume 11, Number 2 (2017), 3165-3195.

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

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Digital Object Identifier

Primary: 62C20: Minimax procedures 62G20: Asymptotic properties
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

Adaptivity Kullback–Leibler divergence nonparametric statistics predictive distribution Stein’s prior

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Yano, Keisuke; Komaki, Fumiyasu. Asymptotically minimax prediction in infinite sequence models. Electron. J. Statist. 11 (2017), no. 2, 3165--3195. doi:10.1214/17-EJS1312. https://projecteuclid.org/euclid.ejs/1505116877

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