메뉴 건너뛰기




Volumn 59, Issue 2, 1996, Pages 249-271

An extension of a convolution inequality for G-monotone functions and an approach to Bartholomew's conjectures

Author keywords

Bartholomew's conjecture; Cone ordering; Convolution inequality; G monotone function; K decreasing function; Majorization; Order restricted alternatives; Reflection; 2 test

Indexed keywords


EID: 0030295593     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1996.0064     Document Type: Article
Times cited : (3)

References (18)
  • 1
    • 84968476146 scopus 로고
    • The integral of a symmetric, unimodal function over a symmetric, convex set and some probability inequalities
    • [1] Anderson, T. W. (1955). The integral of a symmetric, unimodal function over a symmetric, convex set and some probability inequalities. Proc. Amer. Math. Soc. 6 170-176.
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 170-176
    • Anderson, T.W.1
  • 2
    • 0001611337 scopus 로고
    • A test of homogeneity of means under restricted alternatives
    • [2] Bartholomew, D. J. (1961). A test of homogeneity of means under restricted alternatives (with discussion). J. R. Statist. Soc. B 23 239-281.
    • (1961) J. R. Statist. Soc. B , vol.23 , pp. 239-281
    • Bartholomew, D.J.1
  • 4
    • 0001623641 scopus 로고
    • Reflection groups, generalized Schur functions and the geometry of majorization
    • [4] Eaton, M. L., and Perlman, M. D. (1977). Reflection groups, generalized Schur functions and the geometry of majorization. Ann. Probab. 5 829-860.
    • (1977) Ann. Probab. , vol.5 , pp. 829-860
    • Eaton, M.L.1    Perlman, M.D.2
  • 5
    • 21844515017 scopus 로고
    • Monotonicity properties of the power functions of likelihood ratio tests for normal mean hypotheses constrained by a linear space and a cone
    • [5] Hu, X., and Wright, F. T. (1994). Monotonicity properties of the power functions of likelihood ratio tests for normal mean hypotheses constrained by a linear space and a cone. Ann. Statist. 22 1547-1554.
    • (1994) Ann. Statist. , vol.22 , pp. 1547-1554
    • Hu, X.1    Wright, F.T.2
  • 6
    • 0000367034 scopus 로고
    • Majorization in multivariate distributions
    • [6] Marshall, A. W., and Olkin, I. (1974). Majorization in multivariate distributions. Ann. Statist. 2 1189-1200.
    • (1974) Ann. Statist. , vol.2 , pp. 1189-1200
    • Marshall, A.W.1    Olkin, I.2
  • 8
    • 0011632262 scopus 로고
    • The integral of an invariant unimodal function over an invariant convex set - An inequality and applications
    • [8] Mudholkar, G. S. (1966). The integral of an invariant unimodal function over an invariant convex set - An inequality and applications. Proc. Amer. Math. Soc. 17 299-306.
    • (1966) Proc. Amer. Math. Soc. , vol.17 , pp. 299-306
    • Mudholkar, G.S.1
  • 9
    • 0000001456 scopus 로고
    • A probability inequality for elliptically contoured densities with applications in order restricted inference
    • [9] Mukerjee, S. P., Robertson, T., and Wright, F. T. (1986). A probability inequality for elliptically contoured densities with applications in order restricted inference. Ann. Statist. 14 1544-1554.
    • (1986) Ann. Statist. , vol.14 , pp. 1544-1554
    • Mukerjee, S.P.1    Robertson, T.2    Wright, F.T.3
  • 10
    • 0000372698 scopus 로고
    • The likelihood ratio test of normal mean with hypothesis determined by a convex polyhedral cone and the monotonicity of its power function
    • [10] Nomakuchi, K. (1983). The likelihood ratio test of normal mean with hypothesis determined by a convex polyhedral cone and the monotonicity of its power function. Mem. Fac. Sci., Kyushu Univ. A 37 195-209.
    • (1983) Mem. Fac. Sci., Kyushu Univ. A , vol.37 , pp. 195-209
    • Nomakuchi, K.1
  • 12
    • 0001495406 scopus 로고
    • One-sided testing problems in multivariate analysis
    • [12] Perlman, M. D. (1969). One-sided testing problems in multivariate analysis. Ann. Math. Statist. 40 549-567.
    • (1969) Ann. Math. Statist. , vol.40 , pp. 549-567
    • Perlman, M.D.1
  • 13
    • 0000602791 scopus 로고
    • Testing linear hypotheses under restricted alternatives
    • [13] Pincus, R. (1975). Testing linear hypotheses under restricted alternatives. Math. Operationsforsch. Statist. 5 733-751.
    • (1975) Math. Operationsforsch. Statist. , vol.5 , pp. 733-751
    • Pincus, R.1
  • 15
    • 38249013196 scopus 로고
    • On power functions of the likelihood ratio tests for the simple loop order in normal means: Unequal sample sizes
    • [15] Singh, B., and Schell, M. J. (1992). On power functions of the likelihood ratio tests for the simple loop order in normal means: Unequal sample sizes. Statist. Probab. Lett. 14 253-267.
    • (1992) Statist. Probab. Lett. , vol.14 , pp. 253-267
    • Singh, B.1    Schell, M.J.2
  • 16
    • 0000389246 scopus 로고
    • The power functions of the likelihood ratio tests for a simple tree order in normal means: Unequal weights
    • [16] Singh, B., Schell, M. J., and Wright, F. T. (1993). The power functions of the likelihood ratio tests for a simple tree order in normal means: Unequal weights. Commun. Statist. Theor. Methods 22 425-449.
    • (1993) Commun. Statist. Theor. Methods , vol.22 , pp. 425-449
    • Singh, B.1    Schell, M.J.2    Wright, F.T.3
  • 17
    • 84972894654 scopus 로고
    • The power functions of the likelihood ratio tests for a simply ordered trend in normal means
    • [17] Singh, B., and Wright, F. T. (1989). The power functions of the likelihood ratio tests for a simply ordered trend in normal means. Commun. Statist. Theor. Methods 18 2351-2392.
    • (1989) Commun. Statist. Theor. Methods , vol.18 , pp. 2351-2392
    • Singh, B.1    Wright, F.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.