Simultaneous estimation of parameters under entropy loss

Dipak K. Dey; Malay Ghosh; C. Srinivasan

doi:10.1016/0378-3758(86)90108-4

Simultaneous estimation of parameters under entropy loss

Dipak K. Dey, Malay Ghosh, C. Srinivasan

Dr. Bing Zhang Department of Statistics

Research output: Contribution to journal › Article › peer-review

82 Scopus citations

Abstract

The problem considered is simultaneous estimation of scale parameters and their reciprocals from p independent gamma distributions under a scale invariant loss function first introduced in James and Stein (1961). Under mild restrictions on the shape parameters, the best scale invariant estimators are shown to be admissible for p = 2. For p ≥ 3, a general technique is developed for improving upon the best scale invariant estimators. Improvement on the generalized Bayes estimators of a vector involving certain powers of the scale parameter is also obtained.

Original language	English
Pages (from-to)	347-363
Number of pages	17
Journal	Journal of Statistical Planning and Inference
Volume	15
Issue number	C
DOIs	https://doi.org/10.1016/0378-3758(86)90108-4
State	Published - 1986

Bibliographical note

Funding Information:
t The order of the authors' names is alphabetical, and does not indicate their relative contributions to the paper. * Research supported by NSF Grant Number DMS-8218091. ** Research supported by the NSF Grant Number MCS-8212968.

Funding

t The order of the authors' names is alphabetical, and does not indicate their relative contributions to the paper. * Research supported by NSF Grant Number DMS-8218091. ** Research supported by the NSF Grant Number MCS-8212968.

Funders	Funder number
National Science Foundation (NSF)	MCS-8212968, DMS-8218091

Keywords

Admissibility
Best invariant estimators
Differential inequalities
Entropy loss
Gamma scale parameters
Inadmissible estimators
Simultaneous estimation
Trimmed estimators

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1016/0378-3758(86)90108-4

Cite this

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title = "Simultaneous estimation of parameters under entropy loss",

abstract = "The problem considered is simultaneous estimation of scale parameters and their reciprocals from p independent gamma distributions under a scale invariant loss function first introduced in James and Stein (1961). Under mild restrictions on the shape parameters, the best scale invariant estimators are shown to be admissible for p = 2. For p ≥ 3, a general technique is developed for improving upon the best scale invariant estimators. Improvement on the generalized Bayes estimators of a vector involving certain powers of the scale parameter is also obtained.",

keywords = "Admissibility, Best invariant estimators, Differential inequalities, Entropy loss, Gamma scale parameters, Inadmissible estimators, Simultaneous estimation, Trimmed estimators",

author = "Dey, \{Dipak K.\} and Malay Ghosh and C. Srinivasan",

note = "Funding Information: t The order of the authors' names is alphabetical, and does not indicate their relative contributions to the paper. * Research supported by NSF Grant Number DMS-8218091. ** Research supported by the NSF Grant Number MCS-8212968.",

year = "1986",

doi = "10.1016/0378-3758(86)90108-4",

language = "English",

volume = "15",

pages = "347--363",

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T1 - Simultaneous estimation of parameters under entropy loss

AU - Dey, Dipak K.

AU - Ghosh, Malay

AU - Srinivasan, C.

N1 - Funding Information: t The order of the authors' names is alphabetical, and does not indicate their relative contributions to the paper. * Research supported by NSF Grant Number DMS-8218091. ** Research supported by the NSF Grant Number MCS-8212968.

PY - 1986

Y1 - 1986

N2 - The problem considered is simultaneous estimation of scale parameters and their reciprocals from p independent gamma distributions under a scale invariant loss function first introduced in James and Stein (1961). Under mild restrictions on the shape parameters, the best scale invariant estimators are shown to be admissible for p = 2. For p ≥ 3, a general technique is developed for improving upon the best scale invariant estimators. Improvement on the generalized Bayes estimators of a vector involving certain powers of the scale parameter is also obtained.

AB - The problem considered is simultaneous estimation of scale parameters and their reciprocals from p independent gamma distributions under a scale invariant loss function first introduced in James and Stein (1961). Under mild restrictions on the shape parameters, the best scale invariant estimators are shown to be admissible for p = 2. For p ≥ 3, a general technique is developed for improving upon the best scale invariant estimators. Improvement on the generalized Bayes estimators of a vector involving certain powers of the scale parameter is also obtained.

KW - Admissibility

KW - Best invariant estimators

KW - Differential inequalities

KW - Entropy loss

KW - Gamma scale parameters

KW - Inadmissible estimators

KW - Simultaneous estimation

KW - Trimmed estimators

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U2 - 10.1016/0378-3758(86)90108-4

DO - 10.1016/0378-3758(86)90108-4

M3 - Article

AN - SCOPUS:46149142060

SN - 0378-3758

VL - 15

SP - 347

EP - 363

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - C

ER -

Simultaneous estimation of parameters under entropy loss

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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