2012 Fiscal Year Final Research Report
On the effect of the symmetryviolation of loss function to the admissibility of estimation
| Project/Area Number |
21700309
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Statistical science
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
TANAKA Hidekazu 大阪府立大学, 高等教育推進機構, 准教授 (50302344)
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| Research Collaborator |
TATSUKAWA Masashi 大阪府立大学, 大学院・工学研究科
OBAYASHI Chie 大阪府立大学, 大学院・工学研究科
KAMITAMARI Eita 大阪府立大学, 大学院・工学研究科
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| Project Period (FY) |
2009 – 2012
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| Keywords | 統計的推測 / 許容性 / 2次漸近許容性 / 最尤推定量 / 最尤尺度不変推定量 / 形状母数 / 最少ロジットカイ2乗推定量 / ロジスティック回帰モデル |
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| Research Abstract |
Admissibility has been discussed mostly under the quadratic loss function. In this research, first, we derived conditions for estimator to be admissible under asymmetric loss function (linear exponential loss function). On the other hand, in large sample theory it is easy to derive theory since small terms are ignorable. So we considered the asymptotic admissibility of estimator under the normed quadratic loss function. Using these results, we get the (second order) admissibilities or in- admissibilities of the maximum likelihood estimator, minimum logit chi-squared estimator and minimum scale invariant estimator.
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