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Volumn 24, Issue 2, 1996, Pages 753-762

Some Inequalities for symmetric convex sets with applications

Author keywords

Convex sets; Elliptically contoured distributions; Inequalities; Monotonicity of power functions; Unimodal functions

Indexed keywords


EID: 0030494355     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032894463     Document Type: Article
Times cited : (9)

References (13)
  • 1
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    • An optimal property of the Gauss-Markoff estimator
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    • (1990) J. Multivariate Anal. , vol.82 , pp. 171-176
    • Ali, M.M.1    Ponnapalli, R.2
  • 2
    • 84968476146 scopus 로고
    • The integral of a symmetric unimodal function
    • ANDERSON, T. W. (1955). The integral of a symmetric unimodal function. Proc. Amer. Math. Soc. 6 170-176.
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 170-176
    • Anderson, T.W.1
  • 3
    • 0002211598 scopus 로고
    • Nonnormal multivariate distributions: Inference based on elliptically contoured distributions
    • C. R. Rao, ed. North-Holland, Amsterdam
    • ANDERSON, T. W. (1993). Nonnormal multivariate distributions: inference based on elliptically contoured distributions. In Multivariate Analysis: Future Directions (C. R. Rao, ed.) 1-25. North-Holland, Amsterdam.
    • (1993) Multivariate Analysis: Future Directions , pp. 1-25
    • Anderson, T.W.1
  • 4
    • 0039664937 scopus 로고
    • A monotonicity property of the power functions of some tests of the equality of two covariance matrices
    • ANDERSON, T. W. and DAS GUPTA, S. (1964). A monotonicity property of the power functions of some tests of the equality of two covariance matrices. Ann. Math. Statist. 35 1059-1063.
    • (1964) Ann. Math. Statist. , vol.35 , pp. 1059-1063
    • Anderson, T.W.1    Das Gupta, S.2
  • 5
    • 49549132663 scopus 로고
    • On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions and with an application to the diffusion equation
    • BRASCAMP, H. J. and LIEB, E. H. (1976). On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions and with an application to the diffusion equation. J. Funct. Anal. 22 366-389.
    • (1976) J. Funct. Anal. , vol.22 , pp. 366-389
    • Brascamp, H.J.1    Lieb, E.H.2
  • 6
    • 0009401403 scopus 로고
    • Inequalities on the probability context of convex regions for elliptically contoured distributions
    • Univ. California Press, Berkeley
    • DAS GUPTA, S., EATON, M. L., OLKIN, I., PERLMAN, M., SAVAGE, L. J. and SOBEL, M. (1972). Inequalities on the probability context of convex regions for elliptically contoured distributions. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 2 241-265. Univ. California Press, Berkeley.
    • (1972) Proc. Sixth Berkeley Symp. Math. Statist. Probab. , vol.2 , pp. 241-265
    • Das Gupta, S.1    Eaton, M.L.2    Olkin, I.3    Perlman, M.4    Savage, L.J.5    Sobel, M.6
  • 7
    • 38249030530 scopus 로고
    • Concentration inequalities for Gauss-Markov estimators
    • EATON, M. L. (1988). Concentration inequalities for Gauss-Markov estimators. J. Multivariate Anal. 25 119-138.
    • (1988) J. Multivariate Anal. , vol.25 , pp. 119-138
    • Eaton, M.L.1
  • 9
    • 0007233288 scopus 로고
    • T. W. Anderson's theorem on the integral of a symmetric unimodal function over a symmetric convex set and its applications in probability and statistics
    • George P. H. Styan, ed. Wiley, New York
    • PERLMAN, M. D. (1990). T. W. Anderson's theorem on the integral of a symmetric unimodal function over a symmetric convex set and its applications in probability and statistics. In The Collected Papers of T. W. Anderson, 1943-1985 (George P. H. Styan, ed.) 2 1627-1641. Wiley, New York.
    • (1990) The Collected Papers of T. W. Anderson, 1943-1985 , vol.2 , pp. 1627-1641
    • Perlman, M.D.1
  • 10
    • 0002783594 scopus 로고
    • Logarithmic concave measures with applications
    • PRÉKOPA, A. (1971). Logarithmic concave measures with applications. Acta Sci. Math. (Szeged) 32 301-316.
    • (1971) Acta Sci. Math. (Szeged) , vol.32 , pp. 301-316
    • Prékopa, A.1
  • 11
    • 0000485147 scopus 로고
    • On logarithmic concave measures and functions
    • PRÉKOPA, A. (1973). On logarithmic concave measures and functions. Acta Sci. Math. (Szeged) 34 335-343.
    • (1973) Acta Sci. Math. (Szeged) , vol.34 , pp. 335-343
    • Prékopa, A.1
  • 12
    • 0001377577 scopus 로고
    • On convexity of measures
    • RINOTT, Y. (1976). On convexity of measures. Ann. Probab. 4 1020-1026.
    • (1976) Ann. Probab. , vol.4 , pp. 1020-1026
    • Rinott, Y.1
  • 13
    • 0000083925 scopus 로고
    • A theorem on convex sets with applications
    • SHERMAN, S. (1955). A theorem on convex sets with applications. Ann. Math. Statist. 26 926-931.
    • (1955) Ann. Math. Statist. , vol.26 , pp. 926-931
    • Sherman, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.