Estimation after selection from exponential populations with unequal scale parameters

Mohd. Arshad () and Neeraj Misra ()
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Mohd. Arshad: Indian Institute of Technology Kanpur
Neeraj Misra: Indian Institute of Technology Kanpur

Statistical Papers, 2016, vol. 57, issue 3, No 3, 605-621

Abstract: Abstract Consider $$k$$ 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 $$k$$ 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 $$\varphi _{N,1}$$ φ N , 1 and $$\varphi _{N,2}$$ φ N , 2 which are, respectively, based on the maximum likelihood estimators and UMVUEs for component problems. The estimator $$\varphi _{N,2}$$ φ N , 2 is shown to be generalized Bayes. We further show that the UMVUE and the natural estimator $$\varphi _{N,1}$$ φ N , 1 are inadmissible and are dominated by the natural estimator $$\varphi _{N,2}$$ φ N , 2 . A simulation study on the performance of various estimators is also reported.

Keywords: Estimation after selection; Inadmissible estimators; Location parameter; Squared error loss function; UMVU estimator; 62F07; 62F10; 62C15 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-015-0670-6

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