Statistical and computational aspects of shape-constrained inference for covariance function estimation

Oregon Convention Center 

I will introduce nonparametric, shape-constrained estimation 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 \ell_2 consistent estimates of the autocovariance sequence. An algorithm for computing our 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 Matérn covariance as a special case, and I will highlight some possible extensions of shape-constrained approaches for estimating covariance functions in spatial statistics.