ORTHOGONALLY INVARIANT ESTIMATION OF THE SKEW-SYMMETRIC NORMAL MEAN MATRIX

SATOSHI KURIKI

Department of Mathematical Engineering and Information Physics, Faculty of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan

(Received March 3, 1992; revised November 13, 1992)

Abstract. The unbiased estimator of risk of the orthogonally invariant estimator of the skew-symmetric normal mean matrix is obtained, and a class of minimax estimators and their order-preserving modification are proposed. The estimators have applications in paired comparisons model. A Monte Carlo study to compare the risks of the estimators is given.

Key words and phrases: Isotonic regression, minimax estimator, order-pre-serving, paired comparisons, singular value.