| ESTIMATION OF SCATTER MATRIX BASED ON i．i．d． SAMPLE FROM ELLIPTICAL DISTRIBUTIONS |
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| 引用本文： | 方开泰,李润泽. ESTIMATION OF SCATTER MATRIX BASED ON i．i．d． SAMPLE FROM ELLIPTICAL DISTRIBUTIONS[J]. 应用数学学报(英文版), 1995, 11(4): 405-412. DOI: 10.1007/BF02007178 |
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| 作者姓名： | 方开泰 李润泽 |
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| 作者单位： | FANG KAITAI (Institute of APPlied Mathematics,the Chinese Academy of Sciences,Beijing 100080,China and Hong Kong Baptist University,Kowloon,Hong Kong |
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| 摘 要： | ＥＥＳＴＩＭＡＴＩＯＮＯＦＳＣＡＴＴＥＲＭＡＴＲＩＸＢＡＳＥＤＯＮｉ．ｉ．ｄ．ＳＡＭＰＬＥＦＲＯＭＥＬＬＩＰＴＩＣＡＬＤＩＳＴＲＩＢＵＴＩＯＮＳ￥ＦＡＮＧＫＡＩＴＡＩ（方开泰）（ＩｎｓｔｉｔｕｔｅｏｆＡＰＰｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ｔｈｅＣｈｉ...
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| 收稿时间： | 1992-07-28 |
Estimation of scatter matrix based on i.i.d. sample from elliptical distributions |
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| Kaitai Fang,Runze Li. Estimation of scatter matrix based on i.i.d. sample from elliptical distributions[J]. Acta Mathematicae Applicatae Sinica, 1995, 11(4): 405-412. DOI: 10.1007/BF02007178 |
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| Authors: | Kaitai Fang Runze Li |
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| Affiliation: | (1) Institute of Applied Mathematics, the Chinese Academy of Sciences, 100080 Beijing, China;(2) Hong Kong Baptist University, Kowloon, Hong Kong;(3) Prob. Lab., Institute of Applied Mathematics, the Chinese Academy of Sciences, 100080 Beijing, China |
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| Abstract: | In this paper, we consider the estimation of a scatter matrix under entropy loss, quadratic loss, when the samplesx(1),...x(n) are i.i.d. andx(1) ECp( , ,f). With respect to entropy and quadratic losses, we obtain the best estimator of having the form Sx as well as having the formTx Tx , whereSx,Tx and are given in the text, and obtain the minimax estimator of and the best equivariant estimator of with respect to the triangular transformations groupLT+(p) (the group consisting of lower triangular matrices with positive diagonal elements). Some related discussion are given as its generalizations.This work is supported by the National Natural Science Foundation of China and Hong Kong UPGC Grant. |
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| Keywords: | Elliptical distribution entropy loss quadratic loss |
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