A characterization of the multivariate normal distribution and some remarks on linear estimators

Arthur Cohen; Andrew Rukhin; William E. Strawderman

doi:10.1016/0378-3758(87)90126-1

A characterization of the multivariate normal distribution and some remarks on linear estimators

Arthur Cohen, Andrew Rukhin, William E. Strawderman

School of Arts and Sciences, Statistics

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

2 Scopus citations

Abstract

A characterization of the multivariate normal distribution is given. The characterization is essentially based on spherical symmetry and linearity of the posterior mean of a translation parameter vector. In addition some remarks concerning admissibility of linear estimators are made.

Original language	English (US)
Pages (from-to)	361-365
Number of pages	5
Journal	Journal of Statistical Planning and Inference
Volume	17
Issue number	C
DOIs	https://doi.org/10.1016/0378-3758(87)90126-1
State	Published - 1987

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Keywords

Admissibility
Bayes estimator
Characterization
Infinite divisibility
Linear estimation
Multivariate normal
Spherically symmetric distributions

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10.1016/0378-3758(87)90126-1

Cite this

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title = "A characterization of the multivariate normal distribution and some remarks on linear estimators",

abstract = "A characterization of the multivariate normal distribution is given. The characterization is essentially based on spherical symmetry and linearity of the posterior mean of a translation parameter vector. In addition some remarks concerning admissibility of linear estimators are made.",

keywords = "Admissibility, Bayes estimator, Characterization, Infinite divisibility, Linear estimation, Multivariate normal, Spherically symmetric distributions",

author = "Arthur Cohen and Andrew Rukhin and Strawderman, {William E.}",

note = "Funding Information: * Research supported by NSF Grant DMS-84-18416 and NSF Grant DMS-89-01996.",

year = "1987",

doi = "10.1016/0378-3758(87)90126-1",

language = "English (US)",

volume = "17",

pages = "361--365",

journal = "Journal of Statistical Planning and Inference",

issn = "0378-3758",

publisher = "Elsevier B.V.",

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T1 - A characterization of the multivariate normal distribution and some remarks on linear estimators

AU - Cohen, Arthur

AU - Rukhin, Andrew

AU - Strawderman, William E.

N1 - Funding Information: * Research supported by NSF Grant DMS-84-18416 and NSF Grant DMS-89-01996.

PY - 1987

Y1 - 1987

N2 - A characterization of the multivariate normal distribution is given. The characterization is essentially based on spherical symmetry and linearity of the posterior mean of a translation parameter vector. In addition some remarks concerning admissibility of linear estimators are made.

AB - A characterization of the multivariate normal distribution is given. The characterization is essentially based on spherical symmetry and linearity of the posterior mean of a translation parameter vector. In addition some remarks concerning admissibility of linear estimators are made.

KW - Admissibility

KW - Bayes estimator

KW - Characterization

KW - Infinite divisibility

KW - Linear estimation

KW - Multivariate normal

KW - Spherically symmetric distributions

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U2 - 10.1016/0378-3758(87)90126-1

DO - 10.1016/0378-3758(87)90126-1

M3 - Article

AN - SCOPUS:45949121799

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VL - 17

SP - 361

EP - 365

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - C

ER -

A characterization of the multivariate normal distribution and some remarks on linear estimators

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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