1995 Fiscal Year Final Research Report Summary
Relation of the precision of asymptotic expoansions with sample sizes and dimensionality in statistical inference
| Project/Area Number |
06680293
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Statistical science
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| Research Institution | Meisi University |
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Principal Investigator |
SIOTANI Minoru Meisei University, General Educatin, Professor, 一般教育, 教授 (50116597)
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| Co-Investigator(Kenkyū-buntansha) |
IWASHITA Toshiya Science University of Tokyo, Department of Management Sciences, ASssistant Profe, 工学部, 助手 (20266919)
HIRAKAWA Kozaburo Meisei University, General Education, Professor, 一般教育, 教授 (80084367)
UKITA Yoshimasa Meisei University, General Education, Professor, 一般教育, 教授 (70168673)
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| Project Period (FY) |
1994 – 1995
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| Keywords | precision of asymptotic expansion for mula / Hotelling's T^2-test / experimental approximate upper bound / Precision and sample size / OC function and curve / construction method of upper bound / elliptical population / covariance matrix structure / comparison of tests |
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| Research Abstract |
In mulotivariate statistical analysis, the inference procedures are often based on asymptotic expansions for the distributions of key statistics in the underlying inferences. the aim of this research is to search an effective method applicable for the general problem of studying the practical validity of asymptotic expansion formulae used in the statistical inference. In oder to investigate the problem concretely, the asymptotic expansion formula for the OC function of Hotelling's T^2-test was considered.
The OC function depends on the dimensionality p, samplle siza n and noncentrality parameter DELTA. An experimental formula of the approximate upper bound on the absolute error Y of the asymptotic expansion formula for the OC function was obtained, which is a function of p, n and DELTA, that is,
Y<less than or equal>U=0.45702 P^<0.28736> N^<-1.04252>exp{-154232(DELTA-0.39981)}, N=n-p (*)
in D, the reference domain of p, n, DELTA, which was determined concretely. The practical effectivenes
… More
s of this upper bound U was cheked over prameter sets in D.The formula (*)is used to obtain the method of determining a sample size with which a certain requirement on Y or on test. This shows that the construction method of the upper bound on Y is useful and moreover is hopeful to extend its use to other cases ; actually the investigation on the probability of misdiscrimination in the discriminant analysis is now in progress by the similar method.
The results obtained by this research were reported in the annual meetin of Japan statistical Society and Japan-American Joint Meeting on Multivariate Staristical Inference 2000, and the paper will be published in American Journal of Mathematical and Management Sciences.
AS preliminary works on the research project, some results on the T^2 -distribution when the underlying pupulation distribution is elliptical, and on test statistics for testing some multiple comparison hypotheses when the coveriance matrix structure is specific depending on the underlying experimental design. Less
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Research Products
(12 results)
