2004 Fiscal Year Final Research Report Summary
Stein phenomena and further development on shrinkage methods
| Project/Area Number |
13680369
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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 | Japan Women's University (2003-2004)
Chiba University (2001-2002) |
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Principal Investigator |
KONNO Yoshihiko Japan Women's University, Faculty of Science, Associate Professor, 理学部, 助教授 (00205577)
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| Co-Investigator(Kenkyū-buntansha) |
SHIRAISHI Taka-aki Yokohama city University, Department of Mathematical Science, Professor, 大学院・総合理学研究科, 教授 (50143160)
TAKIZAWA Yumi Japan Women's University, Institute of Mathematical Statistics, Department of Prediction and Control, Associate Professor, 統計数理研究所・予測制御系, 助教授 (90280528)
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| Project Period (FY) |
2001 – 2004
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| Keywords | improved estimators / two-sample problems / covariance matrix / simultaneous estimation / growth curve |
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| Research Abstract |
It is well-known that the sample mean and the sample covariance matrix are inadmissible under assumption of normality and appropriate loss function (This is called Stein effect or shrinkage methods.). Since discovery of this phenomenon, there has been a large body of studies on this topic. Furthermore, there has been a broad attention on so called Stein's unbiased risk estimate (SURE), which has been originally proposed for a method to evaluate risk function of estimators under consideration, beyond the original purpose. Although such new development has been reported recently, there are many problems in multivariate analysis with complex structure to be considered based on shrinkage method. The purpose of our research is to develop shrinkage method in complex multivariate model.
In this year we investigate on following statistical models and develop shrinkage estimators :
(1)We have considered the problem of estimating common regression coefficient matrix of two growth curve models and proposed new shrinkage estimators. Furthermore, we demonstrate numerical experiment to indicate that our proposed estimators have better performance over known estimators.
(2)We have considered the problem of estimating a precision matrix of the multivariate normal distribution under the squared loss function and obtained improved estimators.
(3)Applying theory of symmetric cones and generalized Wishart distributions, we have developed improved estimation method including the problem of estimating covariance matrix of complex Wishart distribution.
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