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

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

2010-10-11

arxiv.org/abs/1010.2064v1

Bernoulli 2010, Vol. 16, No. 2, 543-560

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ222 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

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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