Sequential Estimation of a Linear Function of Means of Three Normal Populations

Suppose μi, σi 2 are the mean and variance of the ith normal population, i = 1, 2, 3 (we assume the parameters to be all unknown). For given nonzero constants λ1, λ2, λ3, suppose μ = Σ3 i=1 λiμi. Sequential procedures have been derived (i) to arrive at a fixed width confidence interval for μ, and (ii) to estimate μ pointwise with minimum risk (loss being squared error). Some desirable asymptotic properties are proved for the stopping times in both cases. Monte Carlo studies were made for the problem in (i) with moderate optimal sample sizes.