TY - JOUR
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
SN - 0167-7152
VL - 6
SP - 21
EP - 30
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
IS - 1
ER -