On Asymptotic Risk Efficiency of Point Estimates of Functions of Exponential Scale Parameters by a Two-Stage Sequential Procedure

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 â1 > âL and â2 > âG, where âL, âG > 0 are known to the experimenter from past experiences and look into the estimation of functions of two exponential scale parameters, â = h(â1, â2), where h(â1, â2) 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 (â1/â2)r, r > 0 and \|â1 â â2\|. Simulation results show that on the average, the stopping rule N of the proposed procedure is a good estimate of the optimal sample size nâ, that is, E[N/nâ] a.s. â! 1. Furthermore as c ! 0, the ratio of the risk associated with N and the risk associated with nâ converges to 1, that is, lim c!0RN(c)/Rnâ (c) = 1 suggesting that the two-stage procedure is asymptotically risk efficient.