Project/Area Number  01530018 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
統計学

Research Institution  Science University of Tokyo 
Principal Investigator 
塩谷 實 東京理科大学, 理学部, 教授
SIOTANI Minoru Science University of Tokyo, Professor, 理学部, 教授 (50116597)

CoInvestigator(Kenkyūbuntansha) 
TOMIZAWA Sadao Science University of Tokyo, Lecturer, 理工学部, 助手 (50188778)
KURIKI Shinji Science University of Tokyo, Lecturer (1989) Osaka Women's University, Assistant, 理学部, 講師 (00167389)
SHIMIZU Kunio Science University of Tokyo, Associate Professor, 理工学部, 助教授 (60110946)

Project Fiscal Year 
1989 – 1990

Project Status 
Completed(Fiscal Year 1990)

Budget Amount *help 
¥1,700,000 (Direct Cost : ¥1,700,000)
Fiscal Year 1990 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1989 : ¥900,000 (Direct Cost : ¥900,000)

Keywords  LawleyHotelling's T^2_ / Heteroscedastic method / Maximum of several Hotelling's T^2 / Normallognormal process / Bivariate lognormal distribution / Analysis of square contingency table / Decomposition of model / Existence of designs and balanced complementation / ホテリングT^2分布 / ヘテロセダステイック法 / 数個のホテリングのT^2の最大値 / 正規ー対数定常過程 / 2変量対数正規過程 / 正方分割表解析 / Shannonエントロピ型関連性 / 均斉配列実験計画 / 多重比較 / HotellingのT^2数個の最大値 / 同時信頼区間 / 2変量対数正規分布 / 正規一対数正規定常過程 / 多重分割表 / Shannonエントロピ型関連性尺度 / 楕円型モデルと標本共分散行列 / 2変量デルタ対数正規過程 / 多重分割表の対称モデル構造 / 均斉計画の再帰的構成 / 均斉相補性 / 漸近分散と漸近展開 
Research Abstract 
This research project was supported for two years (1989, 1990) by GrantinAid 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 LawleyHotelling'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^2statistics and their precision by the large scale Monte Carlo numerical experiment. B. For the bivariate lognormal distribution and normallognormal distribution : Exact derivation of variances of ordinary unbiased estimator and its simplified estimator of the crosscovariance function for the normallognormal stationary process ; unbiased estimation of the crosscorrelation coefficients for bivariate Gaussian and normallognormal 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 diagonalsparameter symmetric model, quasiuniform association model, quasidiagonals parameter model. The relations and decompositions of those models are investigated. All theoretical results are checked for the goodnessoffit 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 twise balanced design from some regular twise balanced design ; generalization of the system of equations for the existence of balanced arrays ; relation between rectangular design and balanced array. Less
