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American Journal of Mathematical and Management Sciences Volume 15, 1995 - Issue 3-4: MSI-2000: Multivariate Statistical Analysis in Honor of Professor Minoru Siotani on his 70th Birthday
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Original Articles

Siotani's Contributions to Multivariate Statistical Analysis

Yasunori FujikoshiDepartment of MathematicsHiroshima UniversityHigashi-Hiroshima, 739, Japan
Pages 199-214 | Published online: 14 Aug 2013

  • AndersonT. W. (1984). An Introduction to Multivariate Analysis, Second Edition. John Wiley & Sons, Inc., New York.
  • BartlettM. S. (1938). Further aspects of the theory of multiple regression. Proceedings of the Cambridge Philosophical Society, 34, 30–40.
  • ConstantineA. G. (1963). Some noncentral distribution problems in multivariate analysis. Annals of Mathematical statistics, 34, 1270–1285.
  • Das DuptaS. (1982). Optimum rules for classification into two multivariate normal populations with the same covariance matrix. Handbook of Statistics- 2(KrishnaiahP. K., ed.), North-Holland, New York, 47–60.
  • FujikoshiY. and ShimizuR. (1990). Asymptotic expansions of some distributions and their error bounds - the distributions of sum of independent random variables and scale mixtures. Sugaku Expositions, 3, 75–96.
  • ItoK. (1956). Asymptotic formulae for the distribution of Hotelling's generalized T02 statistic. Annals of Mathematical statistics, 27, 1091–1105.
  • JamesG. S. (1954). Tests of linear hypotheses in univariate and multivariate analysis when the ratios of population variances are unknown. Biometrika, 41, 19–43.
  • JamesA. T. (1964). Distributions of matrix variates and latent roots derived from normal samples. Annals of Mathematical statistics, 35, 475–501.
  • KrishnaiahP. R. (1980). Computations of some multivariate distributions. Handbook of Statistics – 2 (KrishnaiahP. R., ed.), North-Holland, Amsterdam, 745–971.
  • LawleyD. N. (1956). A general method for approximating to the distribution of the likelihood ratio criteria. Biometrika, 43, 295–303.
  • MemomA. Z. and OkamotoM. (1971). Asymptotic expansion of the distribution of the Z statistic in discriminant analysis. Journal of Multivariate Analysis, 1, 294–307.
  • MathaiA. M., ProvostS. B. and HayakawaT. (1995). Bilinear Forms and Zonal Polynomials. Lecture Notes in Statistics, 102, Springer-Verlag, New York.
  • MuirheadR. J. (1982). Aspects of Multivariate Statistical Theory. John Wiley & Sons, Inc., New York.
  • OkamotoM. (1963). An asymptotic expansion for the distribution of the linear discriminant function. Annals of Mathematical statistics, 34, 1286–1301.
  • RaoC. R. (1948). Tests of significance in multivariate analysis. Biometrika,35, 58–78.
  • SiotaniM. (1956). On the distribution of the Hotelling's T2-statistics. Annals of the Institute of Statistical Mathematics, 8, 1–14.
  • SiotaniM. (1957a). Note on the utilization of the generalized Student ratio in the analysis of variance or dispersion. Annals of the Institute of Statistical Mathematics, 9, 157–171.
  • SiotaniM. (1957b). Effects of the additional variate on the canonical correlation coefficients. Proceedings of the Institute of Statistical Mathematics, 5, 52–57, (in Japanese).
  • SiotaniM. (1959). The extreme value of the generalized distances of the individual points in the multivariate normal sample. Annals of the Institute of Statistical Mathematics, 10, 183–208.
  • SiotaniM. (1960). Notes on multivariate confidence bounds. Annals of the Institute of Statistical Mathematics, 11, 167–182.
  • SiotaniM. (1961a). Recent progress in multivariate analysis. Proceedings of the Institute of Statistical Mathematics, 8, 95–142, (in Japanese).
  • SiotaniM. (1961b). The extreme value of generalized distances and its application. Bulletin of International Statistical Institute, 38, 591–599.
  • SiotaniM. (1961c). A note on the interval estimation related to regression matrix. Annals of the Institute of Statistical Mathematics, 12, 147–149.
  • SiotaniM. (1964). Interval estimation for linear combination of means. Journal of the American Statistical Association, 59, 1141–1164.
  • SiotaniM. (1964). Asymptotic distributions of functions of a Wishart matrix. Proceeding of the Institute of Statistical Mathematics, 12, 191–198, (in Japanese).
  • SiotaniM. (1971). An asymptotic expansion of the nonnull distribution of Hotelling's generalized T2-statistic. Annals of Mathematical statistics, 42, 560–571.
  • SiotaniM. and ChouC. (1974). Asymptotic expansion of the nonnull distribution of the ratio of two conditionally independent Hotelling's T2-statistic. Annals of the Institute of Statistical Mathematics, 26, 277–288.
  • SiotaniM. and GengS. (1974). Asymptotic joint distribution of the largest root of several multivariate F matrices, I: quasi-independent case. Journal of Multivariate Analysis, 4, 150–165.
  • SiotaniM. (1975a). Asymptotic expansions for the general distributions of test statistics in multivariate analysis - methods in the recent development I -. Journal of the Japan Statistical Society, 5, 87–103, (in Japanese).
  • SiotaniM. (1975b). Asymptotic expansions of the nonnull distributions of the multivariate test statistics. Modern Courses On Statistical Distributions in Scientific Work – I (PatilG. P., KotzS. and OrdJ. K., eds.), D. Reidel, Boston, 299–317.
  • SiotaniM. (1976). Asymptotic expansions for the general distributions of test statistics in multivariate analysis - methods in the recent development II -. Journal of the Japan Statistical Society, 6, 63–87, (in Japanese).
  • SiotaniM. (1977). Conditional and stepwise multivariate t distributions. Essays in Probability and Statistics (S. Ikeda and others, eds.), Shinko-Tsusho Co. Ltd., Tokyo, 287–303.
  • SiotaniM. and OlkinI. (1977). Asymptotic distribution of functions of a correlation matrix. Essays in Probability and Statistics (S. Ikeda and others, eds.), Shinko-Tsusho Co. Ltd., Tokyo, 235–251.
  • SiotaniM. (1977). Asymptotic expansions for error rates and comparison of the W-procedure and the Z-procedure in discriminant analysis. Multivariate Analysis – IV (KrishnaiahP. K., ed.), North-Holland, New York, 523–545.
  • SiotaniM., DhanwantS. and LöshckeC. (1978). Stepwise test procedures and approximate chi-square analysis. Annals of the Institute of Statistical Mathematics, 30, 365–375.
  • SiotaniM. (1980). Asymptotic approximations to the conditional distributions of the classification statistic Z and its Studentized form Z*. Tamkang Journal of Mathematics 11, 19–32.
  • SiotaniM. (1982). Large sample approximations and asymptotic expansions of classification statistics. Handbook of Statistics – 2 (KrishnaiahP. K., ed.), North-Holland, New York, 61–100.
  • SiotaniM. and FujikoshiY. (1984). Asymptotic approximations for the distributions of multinomial goodness-of-fit statistics. Hiroshima Mathematical Journal, 14, 115–124.
  • SiotaniM., HayakawaT. and FujikoshiY. (1985). Modern Multivariate Statistical Analysis: A Graduate Course and Handbook. American Sciences Press, Inc., Ohio.
  • SiotaniM. (1985). Asymptotic confidence cut-off points in the discriminant analysis with the Studentized statistic Z*. Statistical Theory and Data Analysis(MatusitaK., ed.), North-Holland, New York, 327–340.
  • SiotaniM. and GillD. S. (1987a). The doubly noncentral distribution of Wilks' statistic in MANOVA. Biometrical Journal, 20, 21–29.
  • SiotaniM. and GillD. S. (1987b). On randomization in multivariate analysis of variance. Journal of Statistical Planning and Inference, 17, 217–226.
  • SiotaniM. (1991). Distributions of Lawley-Hotelling's T2 and related statistics: A review. American Journal of Mathematical and Management Sciences, 11, 371–386.
  • SiotaniM. and SeoT. (1992). The multivariate Studentized range and its upper percentile. Journal of the Japan Statistial Society, 22, 123–137.
  • SiotaniM. and SeoT. (1993). Approximation to the upper percentiles of T2max-type statistics. Statistical Sciences and Data Analysis, VST International Sciences Publisher, Zeist, 265–276.
  • SiotaniM. and IwashitaT. (1994). Asymptotic distributions of functions of a sample covariance matrix under the elliptical distribution. The Canadian Journal of Statistics. 22, 273–283.

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