2006 Fiscal Year Final Research Report Summary
New Multivariate-Distribution Estimators in view of Decision Theory
| Project/Area Number |
15530142
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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 |
Economic statistics
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| Research Institution | SHINSHU UNIVERSITY |
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Principal Investigator |
SHEENA Yo SHINSHU UNIVERSITY, Department of Economics, Professor, 経済学部, 教授 (80242709)
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| Project Period (FY) |
2003 – 2006
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| Keywords | unbiasedness / Wishart distribution / orthogonally equivariant estimator / minimax / eigenvalues / covariance matrix / asymptotic distribution / Zonal Polynomials |
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| Research Abstract |
1. We gained the following result on orthogonally equivariant estimators for a non-negative definite random matrix whose density is expanded as a series of zonal polynomials with a non-negative definite matrix parameter.
1) With respect to Stein's loss function, non-order-preserving estimators for the matrix parameter are conjectured to be inadmissible. We proved this for 2-dimensional case.
2) We found an integral inequality on zonal polynomials on the group of orthogonal matrices is a sufficient condition for the above conjecture.
2. Through joint research with Professor Takemura (Tokyo University), we found the following result on an asymptotics when the population eigenvalues of Wishart matrix is infinitely dispersed.
1) Based on the asymptotic distributions which were previously gained, we derived higher-order expansions for those distributions.
2) We derived using the expansions a necessary condition for an estimator of the covariance matrix to be tail-minimax. We applied this result to Stein and Haff estimators and found neither of them is minimax.
3. We considered one-sided test for the null hypothesis that the covariance matrix is equal to a given matrix. The unbiasedness for an invariant test which has a monotone critical region with respect to the eigenvalues was already proved in 60's. We found an alternative proof for the result.
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