Minimax Sequential Procedures for Stochastic Processes

Summary

The problem of finding minimax sequential estimation procedures for stochastic processes is considered. The loss incurred by the statistician is due not only to the error of estimation but also to the cost of observing the process. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The exponential family considered includes many counting, branching, diffusion-type etc. processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of diffusions and counting processes, and for estimating the drift of a geometric Brownian motion.