Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 11, Number 2 (2017), 3165-3195.
Asymptotically minimax prediction in infinite sequence models
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.
Electron. J. Statist. Volume 11, Number 2 (2017), 3165-3195.
Received: June 2016
First available in Project Euclid: 11 September 2017
Permanent link to this document
Digital Object Identifier
Primary: 62C20: Minimax procedures 62G20: Asymptotic properties
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures
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