Admissibility of the natural estimator of the mean of a Gaussian process

AbstractLet {X(t): t ∈ [a, b]} be a Gaussian process with mean μ ∈ L2[a, b] and continuous covariance K(s, t). When estimating μ under the loss ∫ab (μ̂(t)−μ(t))2 dt the natural estimator X is admissible if K is unknown. If K is known, X is minimax with risk ∫ab K(t, t) dt and admissible if and only if the three by three matrix whose entries are K(ti, tj) has a determinant which vanishes identically in ti ∈ [a, b], i = 1, 2, 3