Estimation of scale matrix of elliptically contoured matrix distributions

Run-Ze Li; Kai-Tai Fang

doi:10.1016/0167-7152(94)00186-C

Estimation of scale matrix of elliptically contoured matrix distributions

Run-Ze Li, Kai-Tai Fang^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

2 Citations (Scopus)

Abstract

In this paper, the problem of estimation of scale matrix is considered under entropy loss, quadratic loss and squared error loss. With respect to entropy and quadratic loss, we obtain the best estimator of Σ having the form αS_x as well as having the form T_xΔT_x′, where S_x, T_x and Δ are given in the text, and obtain the minimax estimator of Σ and the best equivariant estimator of Σ with respect to the triangular transformations group. With respect to the squared error loss, we generalize the result of Dey and Srinivasan (1992).

Original language	English
Pages (from-to)	289-297
Number of pages	9
Journal	Statistics and Probability Letters
Volume	24
Issue number	4
DOIs	https://doi.org/10.1016/0167-7152(94)00186-C
Publication status	Published - Sept 1995
Externally published	Yes

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty

User-Defined Keywords

Elliptically matrix distribution
Entropy loss
Quadratic loss
Squared error loss

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10.1016/0167-7152(94)00186-C

Cite this

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abstract = "In this paper, the problem of estimation of scale matrix is considered under entropy loss, quadratic loss and squared error loss. With respect to entropy and quadratic loss, we obtain the best estimator of Σ having the form αSx as well as having the form TxΔTx′, where Sx, Tx and Δ are given in the text, and obtain the minimax estimator of Σ and the best equivariant estimator of Σ with respect to the triangular transformations group. With respect to the squared error loss, we generalize the result of Dey and Srinivasan (1992).",

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T1 - Estimation of scale matrix of elliptically contoured matrix distributions

AU - Li, Run-Ze

AU - Fang, Kai-Tai

PY - 1995/9

Y1 - 1995/9

N2 - In this paper, the problem of estimation of scale matrix is considered under entropy loss, quadratic loss and squared error loss. With respect to entropy and quadratic loss, we obtain the best estimator of Σ having the form αSx as well as having the form TxΔTx′, where Sx, Tx and Δ are given in the text, and obtain the minimax estimator of Σ and the best equivariant estimator of Σ with respect to the triangular transformations group. With respect to the squared error loss, we generalize the result of Dey and Srinivasan (1992).

AB - In this paper, the problem of estimation of scale matrix is considered under entropy loss, quadratic loss and squared error loss. With respect to entropy and quadratic loss, we obtain the best estimator of Σ having the form αSx as well as having the form TxΔTx′, where Sx, Tx and Δ are given in the text, and obtain the minimax estimator of Σ and the best equivariant estimator of Σ with respect to the triangular transformations group. With respect to the squared error loss, we generalize the result of Dey and Srinivasan (1992).

KW - Elliptically matrix distribution

KW - Entropy loss

KW - Quadratic loss

KW - Squared error loss

UR - http://www.scopus.com/inward/record.url?scp=58149212192&partnerID=8YFLogxK

U2 - 10.1016/0167-7152(94)00186-C

DO - 10.1016/0167-7152(94)00186-C

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SN - 0167-7152

VL - 24

SP - 289

EP - 297

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

Estimation of scale matrix of elliptically contoured matrix distributions

Abstract

Scopus Subject Areas

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