Sequential confidence regions for maximum likelihood estimates

The goal of this paper is ti,develop a general framework for constructing s equential fixed size confidence regions based on maximum likelihood estimat es. Asymptotic properties of the sequential procedure for setting up the co nfidence regions are analyzed under very broad assumptions on the underlyin g parametric model. It is shown that the proposed sequential procedure is a symptotically optimal in the sense that it approximates the optimal fixed-s ample size procedure. It is further shown that the "cost of ignorance" asso ciated with the sequential procedure is bounded. Applications are made to e stimation problems arising in prospective and retrospective studies.