When is the pseudo-best estimator blue?

Abstract

SummaryLinear unbiased estimation of the mean of a random variable in Hilbert space is treated in the typical case where the mean belongs to a known subspace.The best linear estimate depends on the underlying covariance operator B0 of the random variable. This operator B0, however, is rarely completely known, so that an auxiliary operator B is used to compute a "pseudo-best" estimate. It is shown that the best and the pseudobest estimates coincide, if and only if BoB -1 leaves M invariant. Applications to linear regression are to be found in the references.