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Bayesian improvements of a MRE estimator of a bounded location parameter. (English) Zbl 1271.62046

Summary: We study the frequentist risk performance of Bayesian estimators of a bounded location parameter, and focus on conditions placed on the shape of the prior density guaranteeing dominance over the minimum risk equivariant (MRE) estimator. For a large class of even and logconcave densities, even convex loss functions, we demonstrate in a unified manner that symmetric priors which are bowled shaped and logconcave lead to Bayesian dominating estimators. The results generalize similar results obtained by E. Marchand and W. E. Strawderman [Ann. Inst. Stat. Math. 57, No. 1, 129–143 (2005; Zbl 1082.62029)] for the fully uniform prior, as well as those obtained by T. Kubokawa [Ann. Stat. 22, No. 1, 290–299 (1994; Zbl 0816.62021)] for squared error loss. Finally, we present a detailed example and several remarks.

MSC:

62F15 Bayesian inference
62F10 Point estimation
62F30 Parametric inference under constraints
62C20 Minimax procedures in statistical decision theory
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References:

[1] Gatsonis, C., MacGibbon, B., & Strawderman, W.E. (1987). On the estimation of a restricted normal mean., Statistics & Probability Letters , 6 , 21-30. · Zbl 0647.62015
[2] Hartigan, J.A. (2004). Uniform priors on convex sets improve risk., Statistics & Probability Letters , 67 , 285-288. · Zbl 1041.62021
[3] Kubokawa, T. (1994). A unified approach to improving on equivariant stimators., Annals of Statistics , 22 , 290-299. · Zbl 0816.62021 · doi:10.1214/aos/1176325369
[4] Kubokawa, T. (2005A). Estimation of bounded location and scale parameters., Journal of the Japanese Statistical Society , 35 , 221-249.
[5] Kubokawa, T. (2005B). Estimation of a mean of a normal distribution with a bounded coefficient of variation, Sankhyā: The Indian Journal of Statistics , 67 , 499-525. · Zbl 1192.62062
[6] Marchand, É. & Perron, F. (2001). Improving on the MLE of a bounded normal mean., Annals of Statistics , 29 , 1078-1093. · Zbl 1041.62016 · doi:10.1214/aos/1013699994
[7] Marchand, É. & Perron, F. (2005). Improving on the MLE of a bounded mean for spherical distributions., Journal of Multivariate Analysis , 92 , 227-238. · Zbl 1062.62101 · doi:10.1016/j.jmva.2003.09.009
[8] Marchand, É. & Perron, F. (2009). Estimating a bounded parameter for symmetric distributions., Annals of the Institute of Mathematical Statistics , 61 , 215-234. · Zbl 1294.62038 · doi:10.1007/s10463-007-0132-6
[9] Marchand, É., Ouassou, I., Payandeh, A.T. & Perron, F. (2008). On the estimation of a restricted location parameter for symmetric distributions., Journal of the Japanese Statistical Society , 38 , 293-309.
[10] Marchand, É. & Strawderman, W.E. (2004). Estimation in restricted parameter spaces: A review., Festschrift for Herman Rubin , IMS Lecture Notes-Monograph Series, 45 , pp. 21-44. · Zbl 1268.62030 · doi:10.1214/lnms/1196285377
[11] Marchand, É. & Strawderman, W.E. (2005A). Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval., Annals of the Institute of Mathematical Statistics , IMS Lecture Notes-Monograph Series, 57 , 129-143. · Zbl 1082.62029 · doi:10.1007/BF02506883
[12] Marchand, É. & Strawderman, W.E. (2005B). On improving on the minimum risk equivariant estimator of a scale parameter under a lower bound constraint, Journal of Statistical Planning and Inference . 134 , 90-101. · Zbl 1067.62025 · doi:10.1016/j.jspi.2004.04.001
[13] van Eeden, C. (2006)., Restricted parameter space problems . Admissibility and minimaxity properties. Lecture Notes in Statistics, 188 , Springer. · Zbl 1160.62018 · doi:10.1007/978-0-387-48809-7
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