Estimation after selection from exponential populations with unequal scale parameters

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• 作者：Mohd. Arshad ; Neeraj Misra
• 关键词：Estimation after selection ; Inadmissible estimators ; Location parameter ; Squared error loss function ; UMVU estimator
• 刊名：Statistical Papers
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：57
• 期：3
• 页码：605-621
• 全文大小：471 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1613-9798
• 卷排序：57

文摘

Consider \(k\) (\(\ge \)2) exponential populations having unknown guarantee times and known (possibly unequal) failure rates. For selecting the unknown population having the largest guarantee time, with samples of (possibly) unequal sizes from the \(k\) populations, we consider a class of selection rules based on natural estimators of the guarantee times. We deal with the problem of estimating the guarantee time of the population selected, using a fixed selection rule from this class, under the squared error loss function. The uniformly minimum variance unbiased estimator (UMVUE) is derived. We also consider two other natural estimators \(\varphi _{N,1}\) and \(\varphi _{N,2}\) which are, respectively, based on the maximum likelihood estimators and UMVUEs for component problems. The estimator \(\varphi _{N,2}\) is shown to be generalized Bayes. We further show that the UMVUE and the natural estimator \(\varphi _{N,1}\) are inadmissible and are dominated by the natural estimator \(\varphi _{N,2}\). A simulation study on the performance of various estimators is also reported.