TY - JOUR
T1 - Truncated linear estimation of a bounded multivariate normal mean
AU - Kortbi, Othmane
AU - Marchand, Éric
N1 - Funding Information:
We are grateful to two anonymous referees for several useful comments and suggestions. The research work of Éric Marchand is partially supported by NSERC of Canada . During Othmane Kortbi's Ph.D. studies at the Université de Sherbrooke, he benefited from financial support from several sources but he wishes to thank especially the ISM (Institut de sciences mathématiques) and the CRM (Centre de recherches mathématiques).
PY - 2012/9
Y1 - 2012/9
N2 - We consider the problem of estimating the mean θ of an N p(θ, I p) distribution with squared error loss ∥δ-θ∥ 2 and under the constraint ∥θ∥≤m, for some constant m>0. Using Stein's identity to obtain unbiased estimates of risk, Karlin's sign change arguments, and conditional risk analysis, we compare the risk performance of truncated linear estimators with that of the maximum likelihood estimator δ mle. We obtain for fixed (m, p) sufficient conditions for dominance. An asymptotic framework is developed, where we demonstrate that the truncated linear minimax estimator dominates δ mle, and where we obtain simple and accurate measures of relative improvement in risk. Numerical evaluations illustrate the effectiveness of the asymptotic framework for approximating the risks for moderate or large values of p.
AB - We consider the problem of estimating the mean θ of an N p(θ, I p) distribution with squared error loss ∥δ-θ∥ 2 and under the constraint ∥θ∥≤m, for some constant m>0. Using Stein's identity to obtain unbiased estimates of risk, Karlin's sign change arguments, and conditional risk analysis, we compare the risk performance of truncated linear estimators with that of the maximum likelihood estimator δ mle. We obtain for fixed (m, p) sufficient conditions for dominance. An asymptotic framework is developed, where we demonstrate that the truncated linear minimax estimator dominates δ mle, and where we obtain simple and accurate measures of relative improvement in risk. Numerical evaluations illustrate the effectiveness of the asymptotic framework for approximating the risks for moderate or large values of p.
KW - Asymptotic analysis
KW - Dominance
KW - Maximum likelihood
KW - Multivariate normal
KW - Point estimation
KW - Restricted parameters
KW - Squared error loss
KW - Truncated linear estimators
KW - Truncated linear minimax
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U2 - 10.1016/j.jspi.2012.03.022
DO - 10.1016/j.jspi.2012.03.022
M3 - Article
AN - SCOPUS:84860884342
SN - 0378-3758
VL - 142
SP - 2607
EP - 2618
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 9
ER -