Sieve Estimator for the Covariance of a Gaussian Process

摘要

Maximum likelihood estimation for the covariance R of a zero-mean Gaussian process is considered, with no assumptions on the covariance or the time parameter set T. It is shown that the likelihood function is a.s. unbounded in general, and a sieve estimator R is constructed. The distribution of R, considered as a process on TxT, can be described exactly if a certain technical assumption is satisfied concerning the bivariate series expansion of R. It is then shown that R (s,t) is asymptotically unbiased and consistent (weakly and in mean square) at each (s,t) is an element of TxT, and that R is strongly consistent (globally) in an appropriate norm.