No abstract

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.

No abstract

No abstract

In many practical situations, it is often desired to select a population (treatment, product, technology, etc.) from a choice of several populations on the basis of a particular characteristic that associated with each population, and then estimate the characteristic associated with the selected population. The present paper is focused on estimating a characteristic of the selected bivariate normal population, using a LINEX loss function. A natural selection rule is used for achieving the aim of selecting the best bivariate normal population. Some natural-type estimators and Bayes estimator (using a conjugate prior) of a parameter of the selected population are presented. An admissible subclass of equivariant estimators, using the LINEX loss function, is obtained. Further, a sufficient condition for improving the competing estimators is derived. Using this sufficient condition, several estimators improving upon the proposed natural estimators are obtained. Further, an application of the derived results is provided by considering the poultry feeds data. Finally, a comparative study on the competing estimators of a parameter of the selected population is carried-out using simulation.