Robustness of a Two-Stage Estimation Procedure when Variances are Unequal

Abstract

We consider two normal populations Π1 and Π2 with means μ1 and μ2 and variances σ2 1 and σ 2 2, respectively, where μ1, μ2, σ 2 1, and σ 2 2 are unknown. Having observed X11, . . . , X1r from Π1 and X21, . . . , X2s from Π2, it is required to estimate μ1 − μ2 by X̄1(r) − X̄2(s) within ±d, where X̄1(r) = 1r ∑r i=1 X1i, X̄2(s) = 1 s ∑s i=1 X2i, and d(> 0) is a given constant. In order to meet such a requirement, we construct a confidence interval