Abstract
In a paper by Lai [(1976) Ann. Statist. 4] a construction of sequences of confidence intervals for one-parameter exponential families is given, where the intersection of these intervals contains the true parameter value θ 0 with a prescribed level of confidence and the respective interval bounds tend a.s. to θ 0. In this paper an analogous result for multiparameter exponential families is proved. More presicely, sequences of convex confidence sets are obtained which shrink to the actual parameter value.
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