Some Inadmissibility Results for Estimating Quantile Vector of Several Exponential Populations with a Common Location Parameter
Keywords:common location, complete class, equivariant estimators, inadmissibility, MLE, quantile estimation, risk comparison, simultaneous estimation, UMVUE
Suppose independent random samples are taken from k (≥ 2) exponential populations with a common and unknown location parameter “µ” and possibly different unknown scale parameters σ1,σ2,...,σk respectively. The estimation of θ = (θ1,θ2,...,θk); where θi is the quantile of the i th population, has been considered with respect to either a sum of squared error loss functions or sum of quadratic losses. Estimators based on maximum likelihood estimators (MLEs) and uniformly minimum variance unbiased estimators (UMVUEs) for each component θi have been obtained. An admissible class of estimators has been obtained. Improvement over an estimator based on UMVUEs is obtained by an application of the Brewster–Zidek technique. Further, classes of equivariant estimators are derived under affine and location groups of transformations and some inadmissibility results are proved. Finally, a numerical comparison of risk performance of all proposed estimators has been done and the recommendations are made for the use of these estimators.
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