Asymptotic minimax risk of predictive density estimation for non-parametric regression

Xinyi Xu, Feng Liang

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)543-560
Number of pages18
JournalBernoulli
Volume16
Issue number2
DOIs
StatePublished - May 2010

Keywords

  • Asymptotic minimax risk
  • Convergence rate
  • Non-parametric regression
  • Pinsker's theorem
  • Predictive density

ASJC Scopus subject areas

  • Statistics and Probability

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