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

Let {X(t): t [set membership, variant] [a, b]} be a Gaussian process with mean [mu] [set membership, variant] L2[a, b] and continuous covariance K(s, t). When estimating [mu] under the loss [integral operator]ab ([mu](t)-[mu](t))2 dt the natural estimator X is admissible if K is unknown. If K is known, X is minimax with risk [integral operator]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 [set membership, variant] [a, b], i = 1, 2, 3.