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Comparison of preliminary test estimators based on generalized order statistics from proportional hazard family using Pitman measure of closeness
Authors:Jafar Ahmadi  Elham Mirfarah  Ahmad Parsian
Affiliation:1. Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, Mashhad, Iran;2. School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Iran
Abstract:In this article, based on generalized order statistics from a family of proportional hazard rate model, we use a statistical test to generate a class of preliminary test estimators and shrinkage preliminary test estimators for the proportionality parameter. These estimators are compared under Pitman measure of closeness (PMC) as well as MSE criteria. Although the PMC suffers from non transitivity, in the first class of estimators, it has the transitivity property and we obtain the Pitman-closest estimator. Analytical and graphical methods are used to show the range of parameter in which preliminary test and shrinkage preliminary test estimators perform better than their competitor estimators. Results reveal that when the prior information is not too far from its real value, the proposed estimators are superior based on both mentioned criteria.
Keywords:Proportional hazard rate model  Preliminary test estimator  Shrinkage preliminary test estimator  Mean squared error  Pitman measure of closeness  Generalized order statistics
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