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

Carl Spruill

Journal of Multivariate Analysis, 1982, vol. 12, issue 4, 568-574

Abstract: 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.

Keywords: Minimax; estimator; infinite; dimensional; mean; Hilbert; space; valued; random; variable (search for similar items in EconPapers)
Date: 1982
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