On an Iterative Algorithm for Sharpening Sathe’s Upper and Lower Bounds on the Variance of UMVU Estimator in Inverse Sampling

by Miodrag M, Ashok Sahai & Neeraj Tiwari.

Abstract: Sathe, Y. S., (1977) found a new set of sharp upper and lower bounds on the variance of the UMVUE in the case of inverse sampling motivated by the fact that a close-form expression to capture the actual variance is unavailable. This note is motivated by their paper and by their inherent desire to capture that variance possibly more closely using their set of the sharp upper and lower bounds. It was very heartening for the authors to realize that the same is possible. In fact the seminal result achieved by the authors in this note could be used for improving the sharpness of these bounds iteratively till it pleases the one using it for the purpose of being close to the actual variance of the UMVUE in the absence of its capture in the closed-form. The achievement is briefly illustrated through a modest empirical study to bring forth the power of the proposed iterative algorithm for the aforesaid purpose. >Key Words: inverse sampling; minimum variance unbiased estimation; success probability; upper & lower variance bounds

Authors:
Ashok Sahai, sahai.ashok@gmail.com
Miodrag M Lovric, mlovric@kg.ac.rs
Neeraj Tiwari, kumarn_amo@yahoo.com

Editor: A.M. Abd-Elfattah,a_afattah@hotmail.com

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