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研究生: 郭信霖
論文名稱: 關於多變量中球狀和主成份特徵値假設檢定之研究
指導教授: 高德超
學位類別: 碩士
Master
系所名稱: 商學院 - 統計學系
Department of Statistics
論文出版年: 1983
畢業學年度: 71
論文頁數: 82
相關次數: 點閱:302下載:0
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  • 第一章 緒論1
    第二章 分配性質的概述7
    第一節 多變量常態的性質7
    第二節 球狀常態的性質10
    第三節 威夏特(Wishart)分配的性質12
    第四節 最大數化(Maximization)14
    第三章 球狀檢定18
    第一節 不變性、不偏性22
    第二節 在H下W的動差25
    第三節 在H下的正確(EXACT)分配31
    第四節 聯集-交集檢定步驟37
    第四章 一些相同性變異數方法和球狀聯立檢定42
    第一節 L₁檢定42
    第二節 巴特雷特(Bartlett)M檢定45
    第三節 球狀聯立檢定48
    第五章 主成份之檢定58
    第一節 Hκ的漸近檢定法59
    第二節 實證分析65
    第六章 結論76
    參考文獻77

    一、中文部份:
    魏應澤著(1982),數理統計學,台北:自印。
    二、英文部份;
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    3. Bishop, D. J. and Nair, U. S. (1939). "A Note On Certain Methods of Testing for The Homogeneity of A Set of Estimated Variances" . J. R. Statist. Soc. Supple. Vol.6, 89-99.
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    11. Gupta, S. D. (1969). "Properties of Power Functions of Some Tests Concerning Dispersion Matrices of Multivariate Normal Distributions", Ann. Math. Statist. Vol. 40. 697-701.
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    13. Hsieh, H. K. (1979). "On Asymptotic Optimality of Likelihood Ratio Tests for Multivariate Normal Distributions". Ann. Statist. Vol.7, 592-598.
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    15. Johnson, R. A. and Wichern, D. W. (1982). "Applied Multivariate Statistical Analysis." (雙葉)
    16. Khatri, C. G. (1978). "Some Optimization Problems with Applications to Canonical Correlations and Sphericity Test". J. Multi. Analy. 453-467.
    17. Krishnaiah, P. R. and Waikar, V. B. (1971). "Simultaneous Tests for Equality of Latent Roots Against Certain Alternatives -I". Ann. Insti. Statist. Math. Vol.23. 451-468.
    18. Krishnaiah, P. R. and Waikar, V. B. (1972). "Simultaneous Tests for Equality of Latents Roots Against Certain Alternatives - II". Ann. Insti. Statist. Math. Vol.24. 81-85.
    19. Knishraiah, P. R. and Schuurman, F. J. (1974). "on the Evaluation of Some Distributions that Arise in Simultaneous Tests for the Equality of the Latent Roots of the Covariance Matrix". J. Multi. Analy. 265-282.
    20. Kshirsagar, A. M. (1961). "The Goodness-of-Fit of a Single Hypothetical Principal Component", Biometrika. Vol. 48. 397-407.
    21. Kshirsagar, A. M. and Gupta, R. P. (1965). "The Goodness of fit of Two (or More) Hypothetical Principal Component". Ann. Insti. Statist. Math. Vol.17. 347-356.
    22. Kshirsagar, A. M. (1972). "Multivariate Analysis". By New York.
    23. Lawley, D. N. (1956). "Tests of Significance for the Latent Roots of the Covariance and Correlation Matrix". Biometrika. Vol.43. 128-136.
    24. Mallows, C. L. (1961). "Latents Vectors of Random Symmetric Matrices", Biometrika. Vol.48, 133-149.
    25. Mardia. K. V. and Kent, J. T. and Bibby, J. M. (1979)". Multivariate Analysis". 華泰
    26. Mauchly, J. W. (1940). "Significance Test for Sphericity of a Normal n-Variate Distribution". Ann. Math. Statist. Vol.11, 204-209.
    27. Mendoza, J. L. (1980). "A Significance Test for Multisample Sphericity". Psychometrika. Vol. 45. 495-498.
    28 . Muirhead , R . J. and Watermaux , C. M. (1980). "Asymptotic Distributions in Canonical Correlation Analysis and other Multivariate Procedures for Nonnormal Population". Biometrika. Vol.67. 31-43.
    29. Muirkead, R. J. (1982). "Aspects of Multivariate Statistical Theory", 華泰
    30. Nagao, H. and Sugiura, N. (1968). "Unbiasedness of Some Test Criteria for the Equality of one or two Covariance Matrices". Ann. Math. Statist. Vol.39. 1686-1692.
    31. Nair. N. S. (1938). "The Application of the Moment Function in the Study of Distribution Laws in Statistics". Biometrika. Vol.30. 274-294.
    32. Olkin, I. and Tomsky, J. L. (1981). "A New Class of Multivariate Tests Based on the Union-Intersection Principle". Ann. Statist. Vol.9. 792-802.
    33. Pearson, K. (1901). "On Lines and Planes of Closect Fit to Systems of Points in Space", Phil. Mag. 2 (Sixth Series) 559-572.
    34. Pitman, E. J. G. (1939). "Test of Hypotheses Concerning Location and Scale Parametersi". Biometrika. Vol. 31. 200-215.
    35. Srivastas, M. S. and Khatri, C. G. (1979). "An Introduction to Multivariate Statistics". By New York.
    36. Steffens, F. E. (1974). "A Bivariate t-Test for Sphericity." S. Afr. Statist. J. Vol.8. 59-68.
    37. Thompson, C. M. and Merrington, M. (1946). "Table for Testing the Homogeneity of a Set of Estimated Variances". Biometrika. Vol.38. 296-304.
    38. Timm, N. H. (1975). Mutlivariate Analysis with Application in Education and Psychology". By New York.
    39. Tyler, D. E. (1981). "Asymptotic Inference for Eigenvectors". Ann. Statist. Vol.9. 725-736.
    40. Venables, W. (1976). "Somes Implications of the Union-Intersection Principle for Tests of Sphericity". J. Multi. Analy. 185-190.
    41. Waternaux, C. M. (1976). "Asymptotic Distribution of the Sample Roots for A Nonnormal Population". Biometrika, Vol. 63. 639-645.
    42. Wilks, S. S. and Thompson, C. M. (1937). "The Sampling Distributions of the Criterion λн₁ When the hypothesis Tested is not True". Biometrika. Vol.29. 124-132.

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