Asymptotic expansions of the estimators in covariance structures with some robustness issues on normal-theory asymptotic cumulants under nonnormality
| Project/Area Number |
18500210
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Otaru University of Commerce |
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Principal Investigator |
OGASAWARA Haruhiko Otaru University of Commerce, Faculty of Commerce, Professor (70271731)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥2,270,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | asymptotic theory / normal theory / robustness / asymptotic cumulants / Studentization / regression analysis / factor analysis / coefficient alpha / 漸近展開 / 非正規分布 / 漸近頑健性 / 統計科学 / エッジワース展開 / 相関係数 |
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| Research Abstract |
(1) Methods of asymptotic expansion
Edgeworth expansion and its variations have been employed as basic tools. Since data in practice are more or less nonnormally distributed, arbitrary distributions including the normal one as a special case are assumed for observable variables.
(2) Asymptotic expansions for the sample correlation coefficient
Asymptotic expansions for the sample correlation coefficient and the sample multiple correlation coefficient are obtained up to order 1/n under nonnormality using the Edgeworth expansion and related methods. Asymptotic robustness of the normal-theory lower-order asymptotic cumulants are also investigated.
(3) Asymptotic expansions in factor analysis
Asymptotic expansions of the non-Studentized estimators and the Studentized ones in factor analysis are given. For Studentization, the sample cumulants up to the fourth order are required and expected to be unstable in finite samples. Considering this property, the Studentized estimators are given under normality and under nonnormality.
(4) Asymptotic expansion for the sample coefficient alpha
The sample coefficient alpha is used as an index of reliability in the behavioral sciences. Reliability indexes are defined for correlation matrices as well as covariance matrices. The expansions of the distributions of the estimators have been derived using the Edgeworth expansion.
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Report
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Research Products
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