1987 Fiscal Year Final Research Report Summary
Structure of Covariance Matrices and Statistical Inference on Them
| Project/Area Number |
61530017
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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 Sceince University of Tokyo, Professor, 理学部, 教授 (50116597)
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| Co-Investigator(Kenkyū-buntansha) |
JINBO Masakazu Science University of Tokyo, Lecturer (Now University of Tsukuba, Assistant Prof, 理工学部, 助手 (50103049)
SATO Manabu Science University of Tokyo, Lecturer, 理学部, 助手 (90178773)
KURIKI Shinji Science University of Tokyo, Lecturer, 理学部, 助手 (00167389)
SHIMIZU Kunio Science University of Tokyo, Associate Professor, 理工学部, 講師 (60110946)
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| Project Period (FY) |
1986 – 1987
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| Keywords | Structure of covariance matrix / Goodness-of fit test / Heteroscedastic method / Improper solution in factor analysis / Stationary lognormal process / Block designs / Existence conditions / 計画配置構成 |
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| Research Abstract |
This reasearch project was supported for two years by Grant-in-Aid for Scientific Research of The Ministry of Education, Science and Culture. The reserch project was conducted no two main areas; (1) multivariate analysis and inferences (M-group), (2) designs and their construction (D-group). Members in each group met once a week and whole members met once a month to discuss and examine results obtained and further progress of researched. Results obtained in the termm of this project are as follows:
M-group: Goodness-of-fit test for the intraclass correlation model; Distributions of statistics, power functions, percentage points, mean and varince of sample size in the multivatiate heterocedastic infernce method; effects by small factors, the continuity properties of solutions, pragmatic check of improper solutions in the factor analysis; Unbiased estimation fo parameters of lognormal distribution and its generalized distribution; Estimation of autocovariance function and autocorrelation coefficient in the statinary lognormal processes.
D-group: Existence conditions of partially balanced arrays in partially balanced fractional factorial designs with 2-symdols; Construction of nested BIB designs based on the t-partition; Mtthod for constructing semi-regular group divisible cyclic designs and thier existence conditions; Some justification of the randomization in multivariate analysis of variance; A product theorem for cyclic graph designs; Equivalence between the existence of 2-symbol balanced arrays of strength t t+2 constraints and the existence of simple arrys of some parameters; Applicability conditions of generalized concept of r-complementation to some block designs.
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Research Products
(42 results)
