Sieve Estimator for the Mean of a Gaussian Process

摘要

A new sieve estimator for the mean function m(t) of a general Gaussian process of known covariance is presented. The estimator m(t) is given explicitly from the data and has a simple distribution. It is shown that m(t) is asymptotically unbiased and consistent (weakly and in mean square) at each t, and that m is strongly consistent for m in an appropriate norm. No assumptions are made about the time parameter or the covariance.