메뉴 건너뛰기




Volumn 34, Issue 1, 1970, Pages 73-144

Asymptotic expansions of the distributions of test statistics in multivariate analysis

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84972535456     PISSN: 00182079     EISSN: None     Source Type: Journal    
DOI: 10.32917/hmj/1206138381     Document Type: Article
Times cited : (52)

References (42)
  • 1
    • 3142617739 scopus 로고
    • The non-central wishart distribution and certain problems of multivariate statistics
    • Anderson, T. W. (1946). The non-central Wishart distribution and certain problems of multivariate statistics. Ann. Math. Statist. 17 409–431.
    • (1946) Ann. Math. Statist , vol.17 , pp. 409-431
    • Anderson, T.W.1
  • 3
    • 4043059000 scopus 로고
    • Monotonicity of the power functions of some tests of independence between two sets of variates
    • Anderson, T. W. and Das Gupta, S. (1964). Monotonicity of the power functions of some tests of independence between two sets of variates. Ann. Math. Statist. 35 206–208.
    • (1964) Ann. Math. Statist , vol.35 , pp. 206-208
    • Anderson, T.W.1    Das Gupta, S.2
  • 4
    • 33846913818 scopus 로고
    • The distribution of the generalized variance
    • Bagai, O. P. (1965). The distribution of the generalized variance. Ann. Math. Statist. 36 120–130.
    • (1965) Ann. Math. Statist , vol.36 , pp. 120-130
    • Bagai, O.P.1
  • 5
    • 0000821797 scopus 로고
    • A general distribution theory for a class of likelihood criteria
    • Box, G.E.P. (1949). A general distribution theory for a class of likelihood criteria. Biometrika 317–346.
    • (1949) Biometrika , pp. 317-346
    • Box, G.E.P.1
  • 6
    • 0001239018 scopus 로고
    • Some non-central distribution problems in, multivariate analysis
    • Constantine, A.G. (1963). Some non-central distribution problems in, multivariate analysis. Ann. Math. Statist. 34 1270–1285.
    • (1963) Ann. Math. Statist , vol.34 , pp. 1270-1285
    • Constantine, A.G.1
  • 8
    • 0005464932 scopus 로고
    • Monotonicity of the power functions of some tests of the multivariate linear hypothesis
    • Das Gupta, S., Anderson, T.W. and Mudholkar, G.S. (1964). Monotonicity of the power functions of some tests of the multivariate linear hypothesis. Ann. Math. Statist. 35 200–205.
    • (1964) Ann. Math. Statist , vol.35 , pp. 200-205
    • Das Gupta, S.1    Erson, T.W.2    Mudholkar, G.S.3
  • 9
    • 84972518118 scopus 로고
    • Asymptotic expansion of the distribution of the generalized variance in the non-central case
    • Fujikoshi, Y. (1968). Asymptotic expansion of the distribution of the generalized variance in the non-central case. J. Sci. Hiroshima Univ. Ser. A-I 32 293–299.
    • (1968) J. Sci. Hiroshima Univ. Ser. A-I , vol.32 , pp. 293-299
    • Fujikoshi, Y.1
  • 10
    • 0040480966 scopus 로고
    • On the distribution of the latent roots of a positive definite random symmetric matrix i
    • Hayakawa, T. (1969). On the distribution of the latent roots of a positive definite random symmetric matrix I. Ann. Inst. Statist. Math. 21 1–21.
    • (1969) Ann. Inst. Statist. Math , vol.21 , pp. 1-21
    • Hayakawa, T.1
  • 11
    • 0000202526 scopus 로고
    • Bessel functions of matrix argument
    • Herz, C. S. (1955). Bessel functions of matrix argument. Ann. of Math. 61 474–523.
    • (1955) Ann. of Math , vol.61 , pp. 474-523
    • Herz, C.S.1
  • 12
    • 0010831911 scopus 로고
    • Generalized asymptotic expansions of cornish-fisher type
    • Hill, G.W. and Davis, A. W. (1968). Generalized asymptotic expansions of Cornish-Fisher type. Ann. Math. Statist. 39 1264–1273.
    • (1968) Ann. Math. Statist , vol.39 , pp. 1264-1273
    • Hill, G.W.1    Davis, A.W.2
  • 13
    • 0002256988 scopus 로고
    • A generalized t test and measure of multivariate dispersion
    • Univ. of California Press
    • Hotelling, H. (1951). A generalized T test and measure of multivariate dispersion. Proc. Second Berkely Symp. Math. Statist. Prob., Univ. of California Press 23–42.
    • (1951) Proc. Second Berkely Symp. Math. Statist. Prob , pp. 23-42
    • Hotelling, H.1
  • 14
    • 0039408334 scopus 로고
    • On generalized analysis of variance (i)
    • Hsu, P. L. (1940). On generalized analysis of variance (I). Biometrika 31 221–237.
    • (1940) Biometrika , vol.31 , pp. 221-237
    • Hsu, P.L.1
  • 15
  • 16
    • 0040000458 scopus 로고
    • 0 statistic. II
    • Ito, K. (1960). Asymptotic formulae for the distribution of Hotelling’s T\ statistic. II. Ann. Math. Statist. 31 1148–1153.
    • (1960) Ann. Math. Statist , vol.31 , pp. 1148-1153
    • Ito, K.1
  • 17
    • 0039408325 scopus 로고
    • A comparison of the powers of two multivariate analysis of variance tests
    • Ito, K. (1962). A comparison of the powers of two multivariate analysis of variance tests. Biometrika 49 455–462.
    • (1962) Biometrika , vol.49 , pp. 455-462
    • Ito, K.1
  • 18
    • 0002416976 scopus 로고
    • Normal multivariate analysis and the orthogonal group
    • James, A. T. (1954). Normal multivariate analysis and the orthogonal group. Ann. Math. Statist. 25 40–75.
    • (1954) Ann. Math. Statist , vol.25 , pp. 40-75
    • James, A.T.1
  • 19
    • 0001154834 scopus 로고
    • The distribution of the latent roots of the covariance matrix
    • James, A. T. (1960). The distribution of the latent roots of the covariance matrix. Ann. Math. Statist. 31 151–158.
    • (1960) Ann. Math. Statist , vol.31 , pp. 151-158
    • James, A.T.1
  • 20
    • 0001679795 scopus 로고
    • Zonal polynomials of the real positive definite symmetric matrices
    • James, Alan T. (1961). Zonal polynomials of the real positive definite symmetric matrices. Ann. of Math. 74 456–469.
    • (1961) Ann. of Math , vol.74 , pp. 456-469
    • James, A.T.1
  • 21
    • 0000952005 scopus 로고
    • Distributions of matrix variates and latent roots derived from normal samples
    • James, Alan T. (1964). Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35 475–501.
    • (1964) Ann. Math. Statist , vol.35 , pp. 475-501
    • James, A.T.1
  • 22
    • 0010999352 scopus 로고
    • Calculation of zonal polynomial coefficients by use of the laplace-beltrami operator
    • James, A. T. (1968). Calculation of zonal polynomial coefficients by use of the Laplace-Beltrami operator. Ann. Math. Statist. 39 1711–1718.
    • (1968) Ann. Math. Statist , vol.39 , pp. 1711-1718
    • James, A.T.1
  • 23
    • 0002619741 scopus 로고
    • Test of linear hypothesis in univariate and multivariate analysis when the ratios of the population variances are unknown
    • James, G. S. (1954). Test of linear hypothesis in univariate and multivariate analysis when the ratios of the population variances are unknown. Biometrika 4-1 19–43.
    • (1954) Biometrika , vol.4-1 , pp. 19-43
    • James, G.S.1
  • 24
    • 0001690797 scopus 로고
    • A generalization of fisher’s z test
    • Lawley, D. N. (1938). A generalization of Fisher’s z test. Biometrika^ 30 180–187.
    • (1938) Biometrika^ , vol.30 , pp. 180-187
    • Lawley, D.N.1
  • 25
    • 84861012826 scopus 로고
    • A comparison of tests of the wilks-lawley hypothesis in multivariate analysis
    • Mikhail, M. N. (1965). A comparison of tests of the Wilks-Lawley hypothesis in multivariate analysis. Biometrika 52 149–156.
    • (1965) Biometrika , vol.52 , pp. 149-156
    • Mikhail, M.N.1
  • 26
    • 84972539230 scopus 로고
    • On the masuyama’s correlation coefficient of vectors
    • (in Japanese)
    • Ogawa, J. (1956). On the Masuyama’s correlation coefficient of vectors. Proc. Inst. Statist. Math. 4 53-60 (in Japanese).
    • (1956) Proc. Inst. Statist. Math , vol.4 , pp. 53-60
    • Ogawa, J.1
  • 27
    • 84972530421 scopus 로고
    • On the distribution of the sum of the roots of a determinantal equation
    • (abstract)
    • Pillai, K. C. S. (1953). On the distribution of the sum of the roots of a determinantal equation. Ann. Math. Statist. 24 495 (abstract).
    • (1953) Ann. Math. Statist , vol.24 , pp. 495
    • Pillai, K.C.S.1
  • 28
    • 0000020001 scopus 로고
    • Some new test criteria in multivariate analysis
    • Pillai, K. C. S. (1955). Some new test criteria in multivariate analysis. Ann. Math. Statist. 26 117–121.
    • (1955) Ann. Math. Statist , vol.26 , pp. 117-121
    • Pillai, K.C.S.1
  • 29
    • 0642346363 scopus 로고
    • On the moments of the trace of a matrix and approximations to its distribution
    • Pillai, K. C. S. and Mijares, T. A. (1959). On the moments of the trace of a matrix and approximations to its distribution. Ann. Math. Statist. 30 1135–1140.
    • (1959) Ann. Math. Statist , vol.30 , pp. 1135-1140
    • Pillai, K.C.S.1    Mijares, T.A.2
  • 30
    • 0014099122 scopus 로고
    • Power comparisons of tests of two multivariate hypotheses based on four criteria
    • Pillai, K. C. S. and Jayachandran, K. (1967). Power comparisons of tests of two multivariate hypotheses based on four criteria. Biometrika 54 195–210.
    • (1967) Biometrika , vol.54 , pp. 195-210
    • Pillai, K.C.S.1    Jayachandran, K.2
  • 31
    • 84932949264 scopus 로고
    • On the moment generating function of pillai’s v criterion
    • Pillai, K. C. S. (1968). On the moment generating function of Pillai’s V criterion. Ann. Math. Statist. 39 877–880.
    • (1968) Ann. Math. Statist , vol.39 , pp. 877-880
    • Pillai, K.C.S.1
  • 32
    • 79952425893 scopus 로고
    • Power of the likelihood-ratio test of the general linear hypothesis in multivariate analysis
    • Posten, H. O. and Bargmann, R. E. (1964). Power of the likelihood-ratio test of the general linear hypothesis in multivariate analysis. Biometrika 51 467–480.
    • (1964) Biometrika , vol.51 , pp. 467-480
    • Posten, H.O.1    Bargmann, R.E.2
  • 33
    • 84913351436 scopus 로고
    • Tests of significance in multivariate analysis
    • Rao, C. R. (1948). Tests of significance in multivariate analysis. Biometrika 35 58–79.
    • (1948) Biometrika , vol.35 , pp. 58-79
    • Rao, C.R.1
  • 34
    • 84950640952 scopus 로고
    • Power of the likelihood-ratio test used in analysis of dispersion
    • edited by P. R. Krishnaiah, Academic Press, New York
    • Roy, J. (1966). Power of the likelihood-ratio test used in analysis of dispersion. Multivariate Analysis, edited by P. R. Krishnaiah, Academic Press, New York. 105–127.
    • (1966) Multivariate Analysis , pp. 105-127
    • Roy, J.1
  • 37
    • 0039413111 scopus 로고
    • Note on the utilization of the generalized student ratio in the analysis of variance or dispersion
    • Siotani, M. (1957). Note on the utilization of the generalized Student ratio in the analysis of variance or dispersion. Ann. Inst. Statist. Math. 9 157–171.
    • (1957) Ann. Inst. Statist. Math , vol.9 , pp. 157-171
    • Siotani, M.1
  • 38
    • 84972524665 scopus 로고
    • Some methods for asymptotic distributions in the multivariate analysis
    • Univ. of North Carolina
    • Siotani, M. (1968). Some methods for asymptotic distributions in the multivariate analysis. Mimeo Series No. 595 Univ. of North Carolina.
    • (1968) Mimeo Series , Issue.595
    • Siotani, M.1
  • 39
    • 0042613493 scopus 로고
    • Asymptotic expansions of the non-null distributions of the likelihood ratio criteria for multivariate linear hypothesis and independence
    • Sugiura, N. and Fujikoshi, Y. (1969). Asymptotic expansions of the non-null distributions of the likelihood ratio criteria for multivariate linear hypothesis and independence. Ann. Math. Statist. 40 942–952.
    • (1969) Ann. Math. Statist , vol.40 , pp. 942-952
    • Sugiura, N.1    Fujikoshi, Y.2
  • 40
    • 0041611606 scopus 로고
    • Asymptotic non-null distributions of the likelihood ratio criteria for covariance matrix under local alternatives
    • Univ. of North Carolina
    • Sugiura, N. (1969). Asymptotic non-null distributions of the likelihood ratio criteria for covariance matrix under local alternatives. Mimeo Series No. 609 Univ. of North Carolina.
    • (1969) Mimeo Series , Issue.609
    • Sugiura, N.1
  • 42
    • 0000921555 scopus 로고
    • Certain generalizations in the analysis of variance
    • Wilks, S. S. (1932). Certain generalizations in the analysis of variance. Biometrika 24 471–494.
    • (1932) Biometrika , vol.24 , pp. 471-494
    • Wilks, S.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.