1990 Fiscal Year Final Research Report Summary
Relations of Covariance-Matrix-Structure of Experimental Designs and Inferences in Multivariate Analysis
| Project/Area Number |
01530018
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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 |
統計学
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| Research Institution | Science University of Tokyo |
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Principal Investigator |
SIOTANI Minoru Science University of Tokyo, Professor, 理学部, 教授 (50116597)
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| Co-Investigator(Kenkyū-buntansha) |
KURIKI Shinji Science University of Tokyo, Lecturer (1989) Osaka Women's University, Assistant, 理学部, 講師 (00167389)
TOMIZAWA Sadao Science University of Tokyo, Lecturer, 理工学部, 助手 (50188778)
SHIMIZU Kunio Science University of Tokyo, Associate Professor, 理工学部, 助教授 (60110946)
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| Project Period (FY) |
1989 – 1990
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| Keywords | Lawley-Hotelling's T^2_ / Heteroscedastic method / Maximum of several Hotelling's T^2 / Normal-lognormal process / Bivariate lognormal distribution / Analysis of square contingency table / Decomposition of model / Existence of designs and balanced complementation |
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| Research Abstract |
This research project was supported for two years (1989, 1990) by Grant-in-Aid Scientific research of The Ministry of Education, Science and Culture. It was regrettable that the investigation on designs of experiment had been forced to discontinue because Dr. Kuriki had moved out to another university. The results obtained in the term of this project are summarized below :
A. For the area of Multivariate Analysis : The mean and variance of sample size in the multivariate heteroscedastic method ; integrated investigation of Lawley-Hotelling's T^2_ and related statistics ; heteroscedastic simultaneous confidence intervals for all double linear compounds of k normal mean vectors and for its subsets, which includes the development of distributions of necessary statistics ; two fundamental formulae for obtaining asymptotic distributions and asymptotic expansions for the functions of a sample covariance matrix under the elliptical population ; formulae for the modified second approximations t
… More
o the upper percentage points of the maximum of several Hotelling's T^2-statistics and their precision by the large scale Monte Carlo numerical experiment.
B. For the bivariate lognormal distribution and normal-lognormal distribution : Exact derivation of variances of ordinary unbiased estimator and its simplified estimator of the cross-covariance function for the normal-lognormal stationary process ; unbiased estimation of the cross-correlation coefficients for bivariate Gaussian and normal-lognormal stationary processes ; Modeling bivariate data containing zeroes based on a bivariate lognormal distribution and derivation of maximum likelihood estimators of parameters, the results of which are applied to daily rainfall data.
C. For the analysis of square contingency tables : For the analysis of square contingency tables with ordered categories, various models of cell probabilities are considered ; symmetry models, conditional symmetry model, linear diagonals-parameter symmetric model, quasi-uniform association model, quasi-diagonals parameter model. The relations and decompositions of those models are investigated. All theoretical results are checked for the goodness-of-fit by using the practical data.
D. For the designs of experiment : A necessary and sufficient condition for the balanced complementation in order to generate a new regular t-wise balanced design from some regular t-wise balanced design ; generalization of the system of equations for the existence of balanced arrays ; relation between rectangular design and balanced array. Less
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