2016 Fiscal Year Final Research Report
New development of statistical estimation on restricted parameters space
| Project/Area Number |
26330047
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Mejiro University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 線形不等式 / 制約条件の下の最尤推定量 / Generalized Bayes 推定量 / 許容的な推定量 / 確率優越性 / Pitman nearness 評価基準 |
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| Outline of Final Research Achievements |
We have obtained two main results: 1) The estimation of two ordered normal means when covariance is known: We have shown that restricted maximum likelihood estimator (RMLE) dominates both estimators proposed by Hwang and Peddada (1994) and Peddada et al. (2005) under stochastic and Pitman nearness criterion. Estimation of linear functions of ordered means is also considered and a necessary and sufficient condition on the coefficients is given for the RMLE to dominate the other estimators under MSE.
2) Simultaneous estimation of p positive normal means when the common variance is unknown: We have studied estimation of several non-negative normal means under sum of squared errors loss when the common variance is unknown. In particular we consider a multivariate shrinkage version of the Katz estimator and show that it dominates the vector version of the Katz estimator which, in the known variance case, is generalized Bayes with respect to the uniform prior over the positive orthant.
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| Free Research Field |
数理統計学
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