Generalized confidence intervals for the largest value of some functions of parameters under normality

This paper deals with generalized confidence intervals (GCIs) for the maxim um value of functions of parameters of interest in the presence of nuisance parameters. For k(greater than or equal to 2) normal populations, we propo se GCIs for, respectively, the largest mean, the largest quantile and the l argest signal-to-noise ratio. For the case of the largest mean, it is shown that the proposed GCIs are be tter than those of Chen and Dudewicz (1973a, b). A new measure of efficienc y is proposed and some Monte Carlo comparisons between the proposed method and the known method are performed. We also show that in several situations the GCIs are equivalent to Bayesian confidence intervals by employing impr oper prior distributions. Illustration is made to some real data.