On the estimation of a restricted normal mean

Constantine Gatsonis; Brenda MacGibbon; William Strawderman

doi:10.1016/0167-7152(87)90054-X

On the estimation of a restricted normal mean

Constantine Gatsonis
, Brenda MacGibbon
, William Strawderman

School of Arts and Sciences, Statistics

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

21 Scopus citations

Abstract

Let X ∼ N(θ,1), where θ ε{lunate} [-m, m], for some m > 0, and consider the problem of estimating θ with quadratic loss. We show that the Bayes estimator δ_m, corresponding to the uniform prior on [-m, m], dominates δ⁰ (x) = x on [-m, m] and it also dominates the MLE over a large part of the parameter interval. We further offer numerical evidence to suggest that δ_m has quite satisfactory risk performance when compared with the minimax estimators proposed by Casella and Strawderman (1981) and the estimators proposed by Bickel (1981).

Original language	English (US)
Pages (from-to)	21-30
Number of pages	10
Journal	Statistics and Probability Letters
Volume	6
Issue number	1
DOIs	https://doi.org/10.1016/0167-7152(87)90054-X
State	Published - Sep 1987

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

bounded normal mean
minimax
uniform prior

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10.1016/0167-7152(87)90054-X

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title = "On the estimation of a restricted normal mean",

abstract = "Let X ∼ N(θ,1), where θ ε\{lunate\} [-m, m], for some m > 0, and consider the problem of estimating θ with quadratic loss. We show that the Bayes estimator δm, corresponding to the uniform prior on [-m, m], dominates δ0 (x) = x on [-m, m] and it also dominates the MLE over a large part of the parameter interval. We further offer numerical evidence to suggest that δm has quite satisfactory risk performance when compared with the minimax estimators proposed by Casella and Strawderman (1981) and the estimators proposed by Bickel (1981).",

keywords = "bounded normal mean, minimax, uniform prior",

author = "Constantine Gatsonis and Brenda MacGibbon and William Strawderman",

note = "Funding Information: * This work was partially supported by NSERC of Canada, FCAR of Quebec and the NSF at MSRI, Berkeley. * * This work was supported by NSF Grant \#DMS 84-18416-01.",

year = "1987",

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doi = "10.1016/0167-7152(87)90054-X",

language = "English (US)",

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T1 - On the estimation of a restricted normal mean

AU - Gatsonis, Constantine

AU - MacGibbon, Brenda

AU - Strawderman, William

N1 - Funding Information: * This work was partially supported by NSERC of Canada, FCAR of Quebec and the NSF at MSRI, Berkeley. * * This work was supported by NSF Grant #DMS 84-18416-01.

PY - 1987/9

Y1 - 1987/9

N2 - Let X ∼ N(θ,1), where θ ε{lunate} [-m, m], for some m > 0, and consider the problem of estimating θ with quadratic loss. We show that the Bayes estimator δm, corresponding to the uniform prior on [-m, m], dominates δ0 (x) = x on [-m, m] and it also dominates the MLE over a large part of the parameter interval. We further offer numerical evidence to suggest that δm has quite satisfactory risk performance when compared with the minimax estimators proposed by Casella and Strawderman (1981) and the estimators proposed by Bickel (1981).

AB - Let X ∼ N(θ,1), where θ ε{lunate} [-m, m], for some m > 0, and consider the problem of estimating θ with quadratic loss. We show that the Bayes estimator δm, corresponding to the uniform prior on [-m, m], dominates δ0 (x) = x on [-m, m] and it also dominates the MLE over a large part of the parameter interval. We further offer numerical evidence to suggest that δm has quite satisfactory risk performance when compared with the minimax estimators proposed by Casella and Strawderman (1981) and the estimators proposed by Bickel (1981).

KW - bounded normal mean

KW - minimax

KW - uniform prior

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U2 - 10.1016/0167-7152(87)90054-X

DO - 10.1016/0167-7152(87)90054-X

M3 - Article

AN - SCOPUS:38249034395

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VL - 6

SP - 21

EP - 30

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 1

ER -

On the estimation of a restricted normal mean

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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