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February 2016 On risk unbiased estimation after selection
Nader Nematollahi, Mohammad Jafari Jozani
Braz. J. Probab. Stat. 30(1): 91-106 (February 2016). DOI: 10.1214/14-BJPS259


In many practical situations, it is desired to compare several populations, find the best one and estimate some parametric functions associated with the selected population. This has been recognized as an important problem that arises in various applications in agricultural, industrial and medical studies. This paper concerns unbiased estimation of a general parametric function, say $\gamma(\theta)$, of selected populations under the squared error loss (SEL) function. Examples of $\gamma(\cdot)$ include reliability function, odds ratio and variance, among others. Also, we obtain the uniformly minimum risk unbiased estimators of the parameters of selected populations under some general class of loss functions other than the commonly used SEL function. Furthermore, we characterize some loss functions for which the risk unbiased estimators of parameters of selected populations do not exist. Theoretical results are augmented with various illustrations and examples.


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Nader Nematollahi. Mohammad Jafari Jozani. "On risk unbiased estimation after selection." Braz. J. Probab. Stat. 30 (1) 91 - 106, February 2016.


Received: 1 March 2014; Accepted: 1 September 2014; Published: February 2016
First available in Project Euclid: 19 January 2016

zbMATH: 1381.62051
MathSciNet: MR3453516
Digital Object Identifier: 10.1214/14-BJPS259

Rights: Copyright © 2016 Brazilian Statistical Association


Vol.30 • No. 1 • February 2016
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