GENERALIZED CONFIDENCE-INTERVALS

The definition of a confidence interval is generalized so that problem s such as constructing exact confidence regions for the difference in two normal means can be tackled without the assumption of equal varian ces. Under certain conditions, the extended definition is shown to pre serve a repeated sampling property that a practitioner expects from ex act confidence intervals. The proposed procedure is also applied to th e problem of constructing confidence intervals for the difference in t wo exponential means and for variance components in mixed models. A re peated sampling property of generalized p values is also given. With t his characterization one can carry out fixed level tests of parameters of continuous distributions on the basis of generalized p values. Fin ally, Pratt's paradox is revisited, and a procedure that resolves the paradox is given.