| Автор | Robert, Christian |
| Дата выпуска | 1989 |
| dc.description | Given a general statistical model and an arbitrary quadratic loss, we propose a lower bound for the associated risk of a class of shrinkage estimators. With respect to the considered class of shrinkage estimators, this bound is optimal.In the particular case of the estimation of the location parameter of an ellipti-cally symmetric distribution, this bound can be used to find the relative improvement brought by a given estimator and the remaining possible improvement, using a Monte-Carlo method. We deduce from these results a new type of shrinkage estimators whose risk can be as close as one wants of the lower bound near a chosen pole and yet remain bounded. Some of them are good alternatives to the positive-part James-Stein estimator. |
| Формат | application.pdf |
| Издатель | Marcel Dekker, Inc. |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Тема | quadratic risk |
| Тема | shrinkage estimators |
| Тема | elliptically symmetric distribution |
| Тема | E-minimaxity |
| Тема | 62C05 |
| Тема | 62C15 |
| Тема | 62F10 |
| Тема | 62J07 |
| Название | A lower bound for the risk of classes of shrinkage estimators ina general multivariate estimation problem and some deduced estimators |
| Тип | research-article |
| DOI | 10.1080/03610928908830036 |
| Electronic ISSN | 1532-415X |
| Print ISSN | 0361-0926 |
| Журнал | Communications in Statistics - Theory and Methods |
| Том | 18 |
| Первая страница | 2289 |
| Последняя страница | 2299 |
| Аффилиация | Robert, Christian; Purdue University and Université de Rouen |
| Выпуск | 6 |
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