Title: Asymptotic properties of pseudo-ML estimators based on covariance approximations
Authors: Reinhard Furrer - University of Zurich (Switzerland) [presenting]
Michael Hediger - University of Zurich (Switzerland)
Abstract: Maximum likelihood (ML) estimators for covariance parameters are highly popular in inference for random fields. In the years, the dataset sizes have steadily increased such that ML approaches can become quite expensive in terms of computational resources. Several covariance approximation approaches have been proposed (e.g., tapering, direct covariance misspecification, low-rank approximation) and have various advantages and disadvantages. We present an approach based on covariance function approximations that are not necessarily positive definite functions. More specifically, for a zero-mean Gaussian random field with a parametric covariance function, we introduce a new notion of likelihood approximations (termed pseudo-likelihood functions), which complements the covariance tapering approach. Pseudo-likelihood functions are based on direct functional approximations of the presumed covariance function. We show that under accessible conditions on the presumed covariance function and covariance approximations, estimators based on pseudo-likelihood functions preserve consistency and asymptotic normality within an increasing-domain asymptotic framework.