Efficient Sequential Estimation in Exponential-Type Processes

Abstract

A class of random processes whose likelihood functions are of exponential type is considered. A necessary and sufficient condition for a stopping time to be efficient (in the Cramer-Rao sense) is proved. This result is obtained after proving a characterization theorem, which asserts that after a suitable random-time transformation such processes become processes with stationary independent increments, by applying the solution of the problem of efficient sequential estimation in the case of processes with stationary independent increments.