Statistica Sinica 10(2000), 1369-1383

GENERALIZED CONFIDENCE INTERVALS FOR THE

LARGEST VALUE OF SOME FUNCTIONS OF

PARAMETERS UNDER NORMALITY

Yi-Ping Chang and Wen-Tao Huang

Soochow University and Tamkang University

Abstract: This paper deals with generalized confidence intervals (GCIs) for the maximum value of functions of parameters of interest in the presence of nuisance parameters. For $k (\ge 2)$ normal populations, we propose GCIs for, respectively, the largest mean, the largest quantile and the largest signal-to-noise ratio.

For the case of the largest mean, it is shown that the proposed GCIs are better than those of Chen and Dudewicz (1973a, b). A new measure of efficiency 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 improper prior distributions. Illustration is made to some real data.

Key words and phrases: Bayesian confidence interval, generalized confidence interval, quantile, signal-to-noise ratio.