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Title On Asymptotic Risk Efficiency of Point Estimates of Functions of Exponential Scale Parameters by a Two-Stage Sequential Procedure
Posted by Bernadette Tubo
Authors Tubo, Bernadette F. and Polestico, Daisy Lou L.
Publication date 2017
Journal Journal of Analysis and Application (JAA)
Volume 15
Issue 2
Pages 133-148
Publisher ISSN:0972-5954; SAS International Publication
Abstract Under the squared error loss plus linear cost, we consider a problem of minimum-risk point estimation of functions of two exponential scale parameters by a two-stage sequential procedure. We assume that  1 >  L and  2 >  G, where  L,  G > 0 are known to the experimenter from past experiences and look into the estimation of functions of two exponential scale parameters,   = h( 1,  2), where h( 1,  2) is a positive real-valued, three-times continuously differential function defined in R2+. The proposed two-stage procedure is shown to enjoy all the usual first-order properties. As a follow-up, we include a simulation study on two specific parameters of the form ( 1/ 2)r, r > 0 and | 1 −  2|. Simulation results show that on the average, the stopping rule N of the proposed procedure is a good estimate of the optimal sample size n , that is, E[N/n ] a.s. −! 1. Furthermore as c ! 0, the ratio of the risk associated with N and the risk associated with n  converges to 1, that is, lim c!0RN(c)/Rn  (c) = 1 suggesting that the two-stage procedure is asymptotically risk efficient.