Abstract Performance bounds for criteria for model selection are developed using recent theory for sieves. The model selection criteria are based on an empirical loss or contrast function with an… Expand

The authors introduce an index of resolvability that is proved to bound the rate of convergence of minimum complexity density estimators as well as the information-theoretic redundancy of the corresponding total description length.Expand

In the absence of knowledge of the true density function, Bayesian models take the joint density function for a sequence of n random variables to be an average of densities with respect to a prior.Expand

We present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy… Expand

We give conditions that guarantee that the posterior probability of every Hellinger neighborhood of the true distribution tends to 1 almost surely. The conditions are (1) a requirement that the prior… Expand

1. Introduction. Consider the estimation of a probability density func- tion p(x) defined on a bounded interval. We approximate the logarithm of the density by a basis function expansion consisting… Expand

We develop and analyze methods for combining estimators from various models for squared-error loss and Gaussian regression with Bayes procedures.Expand