Estimation of the mean of the selected population under asymmetric loss function

Parsian, Ahmad; Farsipour, N. Sanjari

doi:10.1007/s001840050037

Cited by 28 publications

(16 citation statements)

References 15 publications

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“…So, if h(θ) is a random parameter (e.g., θ M , θ J or W), then following Parsian and Sanjari-Farsipour (1999), the estimator…”

Section: Unbiased Estimationmentioning

confidence: 99%

“…For more details and a list of references, see Parsian and Kirmani (2002). For estimating the parameter of selected population under the LINEX loss function, Parsian and Sanjari-Farsipour (1999) and Misra and Mulen (2003) estimate the selected mean of two normal populations with common known variance. They proposed several different estimators of the mean of the largest selected population and compare them numerically.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of the location parameter and the average worth of the selected subset of two parameter exponential populations under LINEX loss function

Nematollahi

Pagheh

2016

Communications in Statistics - Theory and Methods

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Suppose a subset of populations is selected from k exponential populations with unknown location parameters θ 1 , θ 2 , ..., θ k and common known scale parameter σ. We consider the estimation of the location parameter of the selected population and the average worth of the selected subset under an asymmetric LINEX loss function. We show that the natural estimator of these parameters is biased and find the Uniformly Minimum Risk Unbiased (UMRU) estimator of these parameters. In the case of k = 2, we find the minimax estimator of the location parameter of the smallest selected population. Furthermore, we compare numerically the risk of UMRU, minimax and the natural estimators.

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“…So, if h(θ) is a random parameter (e.g., θ M , θ J or W), then following Parsian and Sanjari-Farsipour (1999), the estimator…”

Section: Unbiased Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimation of the location parameter and the average worth of the selected subset of two parameter exponential populations under LINEX loss function

Nematollahi

Pagheh

2016

Communications in Statistics - Theory and Methods

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“…For some of the contributions to problems of estimation after selection, one may refer to Sarkadi (1967), Dahiya (1974), Cohen and Sackrowitz (1982), Sackrowitz and Samul-Cahn (1984), Vellaisamy (1992Vellaisamy ( , 1996Vellaisamy ( , 2009), Misra and Singh (1993), Misra, Anand, and Singh (1998), Parsian and Farsipour (1999), Misra and van der Meulen (2001), Kumar and Tripathi (2003), Kumar and Gangopadhyay (2005), Branden (2006a, 2006b), Kumar, Mahapatra, and Vellaisamy (2009), Motamed-Shariati (2009, 2012), and Al-Mosawi and Vellaisamy (in press). Most of this work was carried out for the situation in which the nuisance parameters and/or sample sizes associated with the given populations are equal.…”

Section: Introductionmentioning

confidence: 97%

Estimation After Selection From Uniform Populations With Unequal Sample Sizes

Arshad

Misra

2015

American Journal of Mathematical and Management Sciences

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Consider k (≥ 2) independent uniform populations π 1 , . . . , π k , where π i ≡ U (0, θ i ), and θ i > 0 (i = 1, . . . , k) is an unknown scale parameter. For selecting the unknown population having the largest scale parameter, we consider a class of selection rules based on the natural estimators of θ i , i = 1, . . . , k. We consider the problem of estimating the scale parameter θ S of the selected population, using a fixed selection rule from this class, under the scaled-squared error loss function. We derive the uniformly minimum variance unbiased estimator (UMVUE) of θ S . We also consider three natural estimators ϕ N ,1 , ϕ N ,2 , and ϕ N ,3 of θ S which are, respectively, based on the maximum likelihood estimators, UMVUEs, and minimum risk equivariant estimators for component estimation problems. The natural estimator ϕ N ,3 is shown to be a generalized Bayes estimator with respect to a non informative prior. Further, we derive a general result for improving a scale-invariant estimator of θ S . Using this result, the estimators better than the UMVUE and the natural estimator ϕ N ,1 are obtained. It is also shown that a subclass of natural-type estimators, which contains the natural estimator ϕ N ,2 , is inadmissible for estimating θ S under the scaled-squared error loss function. Finally, we provide a simulation study on the performances of various competing estimators of θ S .

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“…The problem of estimating a characteristic(s) of the selected population(s) corresponding to the continuous case has been studied in detail in the literature. Some recent references include Kumar and Kar (2001), Kumar and Gangopadhyay (2005), Misra and Meulen (2003), Parsian and Farsipour (1999), Sill and Sampson (2007) and Vellaisamy (2009). The estimation after subset selection for continuous populations has been considered by Panchapakesan (1984, 1986), and Vellaisamy (1992Vellaisamy ( , 1996, among others.…”

Section: Introductionmentioning

confidence: 98%