A note on confidence sequences in multiparameter exponential families

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 θ₀ with a prescribed level of confidence and the respective interval bounds tend a.s. to θ₀. 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.