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Locally minimax tests in symmetrical distributions

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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.

    Article  MathSciNet  Google Scholar 

  • Dawid, A. P. (1977). Spherical matrix distributions and a multivariate model, J. Roy. Statist. Soc. Ser. B, 39, 254–261.

    MathSciNet  MATH  Google Scholar 

  • Dempster, A. P. (1969). Elements of Continuous Multivariate Analysis, Addition Wesley, Reading, Massachusetts.

    MATH  Google Scholar 

  • Eaton, M. L. and Kariya, T. (1981). On a general condition for null robustness, Tech. Report No. 388, University of Minnesota, Mineapolis.

    MATH  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Google Scholar 

  • James, A. T. (1964). The distribution of matrix variates and latent roots derived from normal samples, Ann. Math. Statist., 35, 475–501.

    Article  MathSciNet  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • Kariya, T. (1978). The general Manova problem, Ann. Statist., 6, 200–214.

    Article  MathSciNet  Google Scholar 

  • Kariya, T. (1981). Robustness of multivariate tests, Ann. Statist., 9, 1267–1275.

    Article  MathSciNet  Google Scholar 

  • Kariya, T. and Eaton, M. L. (1977). Robust tests for spherical symmetry, Ann. Statist., 5, 206–215.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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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