Open Access
May 2010 Asymptotic minimax risk of predictive density estimation for non-parametric regression
Xinyi Xu, Feng Liang
Bernoulli 16(2): 543-560 (May 2010). DOI: 10.3150/09-BEJ222


We consider the problem of estimating the predictive density of future observations from a non-parametric regression model. The density estimators are evaluated under Kullback–Leibler divergence and our focus is on establishing the exact asymptotics of minimax risk in the case of Gaussian errors. We derive the convergence rate and constant for minimax risk among Bayesian predictive densities under Gaussian priors and we show that this minimax risk is asymptotically equivalent to that among all density estimators.


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Xinyi Xu. Feng Liang. "Asymptotic minimax risk of predictive density estimation for non-parametric regression." Bernoulli 16 (2) 543 - 560, May 2010.


Published: May 2010
First available in Project Euclid: 25 May 2010

zbMATH: 1345.62065
MathSciNet: MR2668914
Digital Object Identifier: 10.3150/09-BEJ222

Keywords: asymptotic minimax risk , convergence rate , Non-parametric regression , Pinsker’s theorem , predictive density

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

Vol.16 • No. 2 • May 2010
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