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

Let {X(t): t a, b]} be a Gaussian process with mean μ L₂a, b] and continuous covariance K(s, t). When estimating μ under the loss ∫_a^b ( (t)−μ(t))² dt the natural estimator X is admissible if K is unknown. If K is known, X is minimax with risk ∫_a^b K(t, t) dt and admissible if and only if the three by three matrix whose entries are K(t_i, t_j) has a determinant which vanishes identically in t_i a, b], i = 1, 2, 3.