B1770
Title: Statistical and computational aspects of shape-constrained inference for covariance function estimation
Authors: Stephen Berg - Penn State University (United States) [presenting]
Abstract: Nonparametric, shape-constrained estimation is introduced for covariance functions, with an emphasis on a shape-constrained estimator of the autocovariance sequence from a reversible Markov chain. The estimator will be shown to lead to strongly consistent estimates of the asymptotic variance of the sample mean from an MCMC sample, as well as to $l_2$ consistent estimates of the autocovariance sequence. An algorithm for computing the estimator will be presented, and some empirical applications will be shown. The proposed shape-constrained estimator exploits a mixture representation of the autocovariance sequence from a reversible Markov chain. Similar mixture representations exist for stationary covariance functions in spatial statistics, including for the Matern covariance as a special case, and some possible extensions of shape-constrained approaches are highlighted for estimating covariance functions in spatial statistics.
