Equivariant estimation of common location parameter of two exponential populations using censored samples

Abstract

In this paper, we consider the problem of estimating common location parameter of two exponential populations using type-II censored sam- ples when the scale parameters are unknown. The loss function is taken as the quadratic loss. First, we derive a class of ane equivariant esti- mators, which includes the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE). A suf- cient condition for improving estimators in the class is derived. Con- sequently, estimators dominating the MLE and the UMVUE in terms of the risk values are obtained. An example is given to compute the estimates using our result. Finally a simulation study has been carried out to numerically compare the risk functions of all the estimators.