Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location Parameters
We propose improvements under squared error loss of the minimum risk equivariant and the linear minimax estimators for estimating the location parameter θ of a p-variate spherically symmetric distribution, with θ restricted to a ball of radius m centered at the origin. Our construction of explicit...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2010-11-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/93 |
| _version_ | 1798036647106838528 |
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| author | Éric Marchand Amir T. Payandeh Najafabadi |
| author_facet | Éric Marchand Amir T. Payandeh Najafabadi |
| author_sort | Éric Marchand |
| collection | DOAJ |
| description |
We propose improvements under squared error loss of the minimum risk equivariant and the linear minimax estimators for estimating the location parameter θ of a p-variate spherically symmetric distribution, with θ restricted to a ball of radius m centered at the origin. Our construction of explicit improvements relies on a multivariate version of Kubokawa’s Integral Expression of Risk Difference (IERD) method. Applications are given for univariate distributions, for the multivariate normal, and for scale mixture of multivariate normal distributions.
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| first_indexed | 2024-04-11T21:15:45Z |
| format | Article |
| id | doaj.art-5f5fc359f13d487e9a1124a22cfea9b1 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-11T21:15:45Z |
| publishDate | 2010-11-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-5f5fc359f13d487e9a1124a22cfea9b12022-12-22T04:02:49ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712010-11-018210.57805/revstat.v8i2.93Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location ParametersÉric Marchand 0Amir T. Payandeh Najafabadi 1Université de SherbrookeShahid Beheshti University We propose improvements under squared error loss of the minimum risk equivariant and the linear minimax estimators for estimating the location parameter θ of a p-variate spherically symmetric distribution, with θ restricted to a ball of radius m centered at the origin. Our construction of explicit improvements relies on a multivariate version of Kubokawa’s Integral Expression of Risk Difference (IERD) method. Applications are given for univariate distributions, for the multivariate normal, and for scale mixture of multivariate normal distributions. https://revstat.ine.pt/index.php/REVSTAT/article/view/93decision theoryspherical symmetric distributionrestricted parameterminimum risk equivariant estimatorlinear minimax estimatordominating estimators |
| spellingShingle | Éric Marchand Amir T. Payandeh Najafabadi Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location Parameters Revstat Statistical Journal decision theory spherical symmetric distribution restricted parameter minimum risk equivariant estimator linear minimax estimator dominating estimators |
| title | Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location Parameters |
| title_full | Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location Parameters |
| title_fullStr | Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location Parameters |
| title_full_unstemmed | Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location Parameters |
| title_short | Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location Parameters |
| title_sort | improving on minimum risk equivariant and linear minimax estimators of bounded multivariate location parameters |
| topic | decision theory spherical symmetric distribution restricted parameter minimum risk equivariant estimator linear minimax estimator dominating estimators |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/93 |
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