Abstract
In this paper we give an extension of the theory of local minimax property of Giri and Kiefer (1964, Ann. Math. Statist., 35, 21–35) to the family of elliptically symmetric distributions which contains the multivariate normal distribution as a member.
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References
Chielewski, M. A. (1980). Invariance scale matrix hypothesis tests under elliptical symmetry, J. Multivariate Anal., 10, 343–350.
Dawid, A. P. (1977). Spherical matrix distributions and a multivariate model, J. Roy. Statist. Soc. Ser. B, 39, 254–261.
Dempster, A. P. (1969). Elements of Continuous Multivariate Analysis, Addition Wesley, Reading, Massachusetts.
Eaton, M. L. and Kariya, T. (1981). On a general condition for null robustness, Tech. Report No. 388, University of Minnesota, Mineapolis.
Giri, N. (1985a). On a locally best invariant and locally minimax test in symmetrical multivariate distributions, Rapport de recherche No. 85-4, Dép. de mathématiques et de statistique, Univ. de Montréal.
Giri, N. (1985b). Some robust tests of independence in symmetrical distribution, Rapport de recherche No. 85-5, Dép. de mathématiques et de statistique, Univ. de Montréal.
Giri, N. and Kiefer, J. (1964). Local and asymptotic minimax properties of multivariate tests, Ann. Math. Statist., 35, 21–35.
Giri, N. and Sinha, B. (1984). Robust tests of mean vector in symmetrical multivariate distributions, Tech. Report No. 85-01, Center for Multivariate Analysis, University of Pittsburgh.
Gleser, L. J. and Olkin, I. (1970). Linear models in multivariate analysis, Essays in Probability and Statistics, 267–292, Wiley, New York.
James, A. T. (1964). The distribution of matrix variates and latent roots derived from normal samples, Ann. Math. Statist., 35, 475–501.
Jensen, D. R. and Good, I. J. (1981). Invariant distributions associated with matrix laws under structural symmetry, J. Roy. Statist. Soc. Ser. B, 43, 327–332.
Kariya, T. (1978). The general Manova problem, Ann. Statist., 6, 200–214.
Kariya, T. (1981). Robustness of multivariate tests, Ann. Statist., 9, 1267–1275.
Kariya, T. and Eaton, M. L. (1977). Robust tests for spherical symmetry, Ann. Statist., 5, 206–215.
Kariya, T. and Sinha, B. (1984). Nonnull and optimality robustness of some tests, Tech. Report No. 85-01, Center for Multivariate Analysis, University of Pittsburgh.
Schwartz, R. (1967). Local minimax tests, Ann. Math. Statist., 38, 340–360.
Stein, C. (1956). Some problems in multivariate analysis, part 1, Tech. Report No. 6, Statistics Dept., Stanford University.
Wijsman, R. A. (1967). Cross section of Orbits and their applications to densities of maximal invariants, Fifth. Berk. Symp. Math. Stat. Prob., Vol. 1, 389–400, Univ. of California Press.
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This work was partially supported by the Canadian N.S.E.R.C. grant
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Giri, N.C. Locally minimax tests in symmetrical distributions. Ann Inst Stat Math 40, 381–394 (1988). https://doi.org/10.1007/BF00052352
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DOI: https://doi.org/10.1007/BF00052352