Year: 2011
Type: article
Abstract: The frequentist behavior of nonparametric Bayes estimates, more specifically, rates of contraction of the posterior distributions to shrinking Lr-norm neighborhoods, 1 ≤ r ≤ ∞, of the unknown parameter, are studied. A theorem for nonparametric density estimation is proved under general approximation-theoretic assumptions on the prior. The result is applied to a variety of common examples, including Gaussian process, wavelet series, normal mixture and histogram priors. The rates of contraction are minimax-optimal for 1 ≤ r ≤ 2, but deteriorate as r increases beyond 2. In the case of Gaussian nonparametric regression a Gaussian prior is devised for which the posterior contracts at the optimal rate in all Lr-norms, 1 ≤ r ≤ ∞.
Source: The Annals of Statistics
Authors: Evarist Giné, Richard Nickl
Institutions: University of Connecticut, University of Cambridge
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1490700875