Abstract
In this paper we will study the asymptotic behavior of tail probability of the sequential maximum likelihood estimator for the exponential class. This class contains many important stochastic processes including the Wiener process, Bernoulli process, Poisson process, gamma process, and Gaussian autoregressive process, etc. We introduce a stopping time which is useful in sequential statistical analysis. It is shown that the tail probability of the sequential maximum likelihood estimator based on the stopping time decreases exponentially fast as the stopping boundary diverges, and some examples are verified.
