Information inequalities in a general sequential model for stochastic processes are presented by applying the approach to estimation through estimating functions. Using this approach, Bayesian versions of the information inequalities are also obtained. In particular, exponential-family processes...

Information inequalities in a general sequential model for stochastic processes are presented by applying the approach to estimation through estimating functions. Using this approach, Bayesian versions of the information inequalities are also obtained. In particular, exponential-family processes...

The study of the theory of sequential estimation for continuous-time stochastic processes was initiated by Dvoretzky, Kiefer and Wolfowitz (1953). They proved that for the Poisson, negative-binomial, gamma and Wiener processes the minimax sequential plan reduces to a fixed-time plan if a...