Asymptotic minimax risk of predictive density estimation for non-parametric regression
Statistics Theory
2010-10-12 v1 Statistics Theory
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.
Cite
@article{arxiv.1010.2064,
title = {Asymptotic minimax risk of predictive density estimation for non-parametric regression},
author = {Xinyi Xu and Feng Liang},
journal= {arXiv preprint arXiv:1010.2064},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.3150/09-BEJ222 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)