OPTIMAL CONFIDENCE INTERVALS FOR THE LARGEST LOCATION PARAMETER

Summary. Suppose that Π 1 , Π 2 , …, Π k are k given populations (k ≥ 1) with location parameters θ 1 , θ 2 , …, θ k , respectively, T is an appropriate statistic with density g(y, θ) = g(y−θ), and t 1 , t 2 , …, t k is the set of observed T values from Π 1 , Π 2 , …, Π k respectively. In this paper we consider an optimal confidence interval of the form I = (t*−(L−d), t*+d) for the largest location parameter θ* = . based on t* = . Under certain assumptions on g we have obtained a general least favorable (LF) configuration for I. For a given L (the length of I), we have proved that the d value which maximizes the coverage probability of I under the LF configuration is equal to L/2 for k = 1, 2 and less than L/2 for k > 2. Tables are given, for normal populations, of this optimal value of d and the corresponding coverage probabilities.