Electronic Journal of Statistics

Asymptotically minimax prediction in infinite sequence models

Keisuke Yano and Fumiyasu Komaki

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1505116877

Digital Object Identifier
doi:10.1214/17-EJS1312

Mathematical Reviews number (MathSciNet)
MR3697133

Zentralblatt MATH identifier
1373.62039

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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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