Note on the utilization of the generalized student ratio in the analysis of variance or dispersion

Siotani, Minoru

doi:10.1007/bf02892503

Cited by 24 publications

(13 citation statements)

References 5 publications

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“…In this case the limiting distribution of F 0 is (r/q)Fpq,pr· By using the same technique as in the case of Ti, asymptotic expansions up to the order n-2 were obtained for the percent point and the nonnull distribution of F 0 by Siotani (1957a) and Chou and Siotani (1974), respectively.…”

Section: Hotelling's Generalized T~-statisticmentioning

confidence: 98%

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Siotani's Contributions to Multivariate Statistical Analysis

Fujikoshi

1995

American Journal of Mathematical and Management Sciences

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Section: Hotelling's Generalized T~-statisticmentioning

confidence: 98%

“…Siotani (1957a) first obtained an asymptotic expansion for the nonull distribution of Hotelling's generalized Tg-statistic. It may be noted that the papers mentioned above have had an important influence on much subsequent work on asymptotic expansions.…”

Section: Introductionmentioning

confidence: 99%

Siotani's Contributions to Multivariate Statistical Analysis

Fujikoshi

1995

American Journal of Mathematical and Management Sciences

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“…Box [5] derived an asymptotic expansion of the null distribution of T LR . Asymptotic expansions of the null and nonnull distributions of T LH were given by Siotani [97,98] and Ito [72,73]. The moment of T LR was obtained by Constantine [6] in terms of the hypergeometric function 1 F 1 of the matrix argument, which is a power series of zonal polynomials reported by James [74,75].…”

Section: Asymptotic Expansions For Major Multivariate Test Statisticsmentioning

confidence: 99%

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Siotani

Wakaki

2006

Journal of Multivariate Analysis

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The purpose of this article is to review the findings of Professor Fujikoshi which are primarily in multivariate analysis. He derived many asymptotic expansions for multivariate statistics which include MANOVA tests, dimensionality tests and latent roots under normality and nonnormality. He has made a large contribution in the study on theoretical accuracy for asymptotic expansions by deriving explicit error bounds. A large contribution has been also made in an important problem involving the selection of variables with introducing "no additional information hypotheses" in some multivariate models and the application of model selection criteria. Recently he is challenging to a high-dimensional statistical problem. He has been involved in other topics in multivariate analysis, such as power comparison of a class of tests, monotone transformations with improved approximations, etc.

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“…Utilizing the asymptotic expansion of the distribution function of qZ with ZtF q, r as given in Siotani (1957), we obtain the following from (4.4) by inversely transforming the characteristic function: For x>0, we write…”

Section: Equal Intraclass Correlation Matrixmentioning

confidence: 99%

Fixed-Width Simultaneous Confidence Intervals for Multinormal Means in Several Intraclass Correlation Models

Aoshima

Mukhopadhyay

1998

Journal of Multivariate Analysis

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The problem of constructing fixed-width simultaneous confidence intervals for comparing mean vectors of k( 2) independent multivariate normal distributions is considered when those covariance matrices have the intraclass correlation structures. Two-stage procedures are developed for which the simultaneous confidence levels are shown to be at least 1&:, the preassigned nominal value, 0<:<1. Asymptotic efficiency properties are addressed. In the case of fixed and finite initial sample size, efficiency related issues are also discussed. Academic PressAMS 1991 subject classifications: 62L05, 62H99, 62J15.

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Note on the utilization of the generalized student ratio in the analysis of variance or dispersion

Cited by 24 publications

References 5 publications

Siotani's Contributions to Multivariate Statistical Analysis

Siotani's Contributions to Multivariate Statistical Analysis

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Fixed-Width Simultaneous Confidence Intervals for Multinormal Means in Several Intraclass Correlation Models

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