Estimation after selection from exponential populations with unequal scale parameters

Arshad, Mohd Anuar; Misra, Neeraj

doi:10.1007/s00362-015-0670-6

Cited by 15 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Estimation following selection problems involving exponential populations have particularly attracted the attention of many researchers. Some of the worth mentioning contributions in this direction are due to Misra and Singh (1993), Misra et al (1998), Vellaisamy (2003), Kumar and Kar (2001) and Arshad and Misra (2016). Misra and Singh (1993) considered the problem of estimation of location parameter of the selected exponential population from k (≥ 2) exponential population having different unknown location parameters but a common known scale parameter.…”

Section: Introductionmentioning

confidence: 99%

“…Misra and Singh (1993) considered the problem of estimation of location parameter of the selected exponential population from k (≥ 2) exponential population having different unknown location parameters but a common known scale parameter. Arshad and Misra (2016) considered the case of known and, possibly, unequal scale parameters and derived some decision theoretic results for the problem of estimating the location parameter of the population selected from k (≥ 2) populations. Kumar and Kar (2001) considered the problem of estimating quantiles of a selected exponential population with a common location parameter and different scale parameters.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Equivariant Estimation of the Selected Guarantee Time

Masihuddin¹,

Misra²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Consider two independent exponential populations having different unknown location parameters and a common unknown scale parameter. Call the population associated with the larger location parameter as the "best" population and the population associated with the smaller location parameter as the "worst" population. For the goal of selecting the best (worst) population a natural selection rule, that has many optimum properties, is the one which selects the population corresponding to the larger (smaller) minimal sufficient statistic. In this article, we consider the problem of estimating the location parameter of the population selected using this natural selection rule. For estimating the location parameter of the selected best population, we derive the uniformly minimum variance unbiased estimator (UMVUE) and show that the analogue of the best affine equivariant estimators (BAEEs) of location parameters is a generalized Bayes estimator. We provide some admissibility and minimaxity results for estimators in the class of linear, affine and permutation equivariant estimators, under the criterion of scaled mean squared error. We also derive a sufficient condition for inadmissibility of an arbitrary affine and permutation equivariant estimator. We provide similar results for the problem of estimating the location parameter of selected population when the selection goal is that of selecting the worst exponential population. Finally, we provide a simulation study to compare, numerically, the performances of some of the proposed estimators.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Equivariant Estimation of the Selected Guarantee Time

Masihuddin¹,

Misra²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the literature such problems are termed as estimation after selection problems. For references on these problems, see: Misra and Dhariyal (1994), Vellaisamy (1996Vellaisamy ( , 2009, Anand, Misra, and Singh (1998), Misra and van der Meulen (2001), Kumar and Tripathi (2003), Misra and Arshad (2014), Arshad, Misra, and Vellaisamy (2015), Arshad and Misra (2016), Nematollahi and Jozani (2016), Arshad and Abdalghani (in press). Vellaisamy, Somesh, and Divakar (1988) studied the problem of estimation after selection from the uniform population under the assumption of equal sample sizes and the squared error loss function.…”

Section: Introductionmentioning

confidence: 99%

Estimation after Selection from Uniform Populations under an Asymmetric Loss Function

Arshad

Abdalghani

2019

American Journal of Mathematical and Management Sciences

Self Cite

View full text Add to dashboard Cite

The problem of estimation after selection arises in the situations where we wish to select a population among k available populations and estimate the parameter of the selected population. This paper considers estimation of the scale parameter h S of the selected uniform population, under the criterion of an asymmetric scale equivariant (ASE) loss function. For selecting the best uniform population, a class of selection rules proposed by Arshad and Misra (2015b) is used. Three natural estimators of h S based on the maximum likelihood estimators, uniformly minimum variance unbiased estimators, and minimum risk equivariant estimators are considered. The generalized Bayes estimator of h S with respect to a non-informative prior is derived. Under the ASE loss function, a general result for improving a scale-equivariant estimator of h S is provided. A consequence of this result, the estimators better than some of the natural estimators are obtained. Also, under the ASE loss function, a subclass of natural-type estimators is shown to be inadmissible for estimating h S. Finally, the risk functions of the various competing estimators of h S are compared via a simulation study.

show abstract

Estimating moments of a selected Pareto population under asymmetric scale invariant loss function

Al-Mosawi

Khan

2016

Stat Papers

View full text Add to dashboard Cite

Consider independent random samples from (k ≥ 2) Pareto populations with the same known shape parameter but different scale parameters. Let X i be the smallest observation of the ith sample. The natural selection rule which selects the population associated with the largest X i is considered. In this paper, we estimate the moments of the selected population under asymmetric scale invariant loss function. We investigate risk-unbiased, consistency and admissibility of the natural estimators for the moments of the selected population. Finally, the risk-bias's and risks of the natural estimators are numerically computed and compared for k = 2, 3.

show abstract

Estimation after selection from exponential populations with unequal scale parameters

Cited by 15 publications

References 25 publications

Equivariant Estimation of the Selected Guarantee Time

Equivariant Estimation of the Selected Guarantee Time

Estimation after Selection from Uniform Populations under an Asymmetric Loss Function

Estimating moments of a selected Pareto population under asymmetric scale invariant loss function

Contact Info

Product

Resources

About