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.
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References
David, H. A. (1988).The Method of Paired Comparisons, 2nd ed., Charles Griffin & Company Limited, London.
Khatri, C. G. (1965). A test for reality of a covariance matrix in a certain complex Gaussian distribution,Ann. Math. Statist. 36, 115–119.
Kuriki, S. (1992). Simultaneous inference on interactions in paired comparisons: An application of the distribution of singular values of skew-symmetric random matrix, METR, 92-13, Department of Mathematical Engineering and Information Physics, University of Tokyo.
Robertson, T., Wright, F. T. and Dykstra, R. L. (1988).Order Restricted Statistical Inference, Wiley, Chichester.
Scheffé, H. (1952). An analysis of variance for paired comparisons,J. Amer. Statist. Assoc.,47, 381–400.
Sheena, Y. (1991). Unpublished lecture note, University of Tokyo.
Sheena, Y. and Takemura, A. (1992). Inadmissibility of non-order-preserving orthogonally invariant estimators of the covariance matrix in the case of Stein's loss,J. Multivariate Anal.,41, 117–131.
Stein, C. (1973). Estimation of the mean of a multivariate normal distribution,Proc. Prague Symp. on Asymptotic Statistics, 345–381.
Stein, C. (1981). Estimation of the mean of a multivariate normal distribution,Ann. Statist.,9, 1135–1151.
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Kuriki, S. Orthogonally invariant estimation of the skew-symmetric normal mean matrix. Ann Inst Stat Math 45, 731–739 (1993). https://doi.org/10.1007/BF00774784
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DOI: https://doi.org/10.1007/BF00774784