# Gamma-minimax estimators in the exponential family

Lanxiang Chen; Heike Hofmann; Jürgen Eichenauer-Herrmann; Jürgen Kindler

- Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1991

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topLanxiang Chen, et al. Gamma-minimax estimators in the exponential family. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1991. <http://eudml.org/doc/219358>.

@book{LanxiangChen1991,

abstract = {The Γ-minimax estimator under squared error loss for the unknown parameter of a one-parameter exponential family with an unbiased sufficient statistic having a variance which is quadratic in the parameter is explicitly determined for a class Γ of priors consisting of all distributions whose first two moments are within some given bounds. This generalizes the choice of Γ in Jackson et al. (1970) as well as the unrestricted case. It is shown that the underlying statistical game is always strictly determined and that there exists a Γ-minimax estimator which is a linear function of the unbiased sufficient statistic. If the bounds for both prior moments are effective then there exists a least favourable prior in Γ which is a member of the Pearsonian family.CONTENTS1. Introduction and summary....................52. A class of exponential families..............63. The estimation problem......................124. Solution of the statistical games.........175. Some special cases............................326. Concluding remark.............................33References............................................351980 Mathematics Subject Classification: (1985 Revision): Primary 62C99; Secondary 62F10.},

author = {Lanxiang Chen, Heike Hofmann, Jürgen Eichenauer-Herrmann, Jürgen Kindler},

keywords = {Gamma-minimax; exponential family; squared error loss; moment restrictions; least favourable; conjugate prior; Pearsonian family; gamma-minimax estimator; one-parameter exponential family; unbiased sufficient statistic; natural conjugate priors; Bayes estimators; Bayes risk; moments; statistical game},

language = {eng},

location = {Warszawa},

publisher = {Instytut Matematyczny Polskiej Akademi Nauk},

title = {Gamma-minimax estimators in the exponential family},

url = {http://eudml.org/doc/219358},

year = {1991},

}

TY - BOOK

AU - Lanxiang Chen

AU - Heike Hofmann

AU - Jürgen Eichenauer-Herrmann

AU - Jürgen Kindler

TI - Gamma-minimax estimators in the exponential family

PY - 1991

CY - Warszawa

PB - Instytut Matematyczny Polskiej Akademi Nauk

AB - The Γ-minimax estimator under squared error loss for the unknown parameter of a one-parameter exponential family with an unbiased sufficient statistic having a variance which is quadratic in the parameter is explicitly determined for a class Γ of priors consisting of all distributions whose first two moments are within some given bounds. This generalizes the choice of Γ in Jackson et al. (1970) as well as the unrestricted case. It is shown that the underlying statistical game is always strictly determined and that there exists a Γ-minimax estimator which is a linear function of the unbiased sufficient statistic. If the bounds for both prior moments are effective then there exists a least favourable prior in Γ which is a member of the Pearsonian family.CONTENTS1. Introduction and summary....................52. A class of exponential families..............63. The estimation problem......................124. Solution of the statistical games.........175. Some special cases............................326. Concluding remark.............................33References............................................351980 Mathematics Subject Classification: (1985 Revision): Primary 62C99; Secondary 62F10.

LA - eng

KW - Gamma-minimax; exponential family; squared error loss; moment restrictions; least favourable; conjugate prior; Pearsonian family; gamma-minimax estimator; one-parameter exponential family; unbiased sufficient statistic; natural conjugate priors; Bayes estimators; Bayes risk; moments; statistical game

UR - http://eudml.org/doc/219358

ER -

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