The approximation rate and the parsimony of the parameterization of the networks are shown to be advantageous in high-dimensional settings and the integrated squared approximation error cannot be made smaller than order 1/n/sup 2/d/ uniformly for functions satisfying the same smoothness assumption.Expand

It is shown that the quadratic risk of the minimum penalized empirical contrast estimator is bounded by an index of the accuracy of the sieve, which quantifies the trade-off among the candidate models between the approximation error and parameter dimension relative to sample size.Expand

The normalized maximized likelihood, mixture, and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms.Expand

An index of resolvability 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 to demonstrate the statistical effectiveness of the minimum description-length principle as a method of inference.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

The authors examine the relative entropy distance D/sub n/ between the true density and the Bayesian density and show that the asymptotic distance is (d/2)(log n)+c, where d is the dimension of the parameter vector.Expand

Analogous convergence results for the relative entropy are shown to hold in general, for any class of log-density functions and sequence of finite-dimensional linear spaces having L2 and L.Expand

An unbiased estimator of the risk of the mixture of general estimators is developed and the performance of these mixture estimator is better than that of a related model-selection estimator which picks a model with the highest weight.Expand