Unbiased Estimation of the Common Mean of Two Normal Distributions Based on Small Samples of Equal Size

Abstract Given two independent simple random samples of equal size from two normal distributions, N(μ, σ2 i ) (i = 1, 2), the problem is to estimate the common mean μ, — ∞ ρ and by if S 2/S 1 < 1/ρ*. The variances and the efficiency functions of these estimators are studied. Explicit formulae are given for the case of samples of size n = 3. Recommendations are made for a robust estimation procedure.