Asymptotic minimaxity of a sequential estimator for a first order autoregressive model

Abstract

A result of Lai and Siegmund [7] says that certain sequential estimates, using the method of least squares, of the parameter in the first order autoregressive model , have the property of uniform asymptotic normality for . We prove weak convergence of statistical experiments associated with the first order autoregressive model, using convergence of Hellinger processes, and show that sequential maximum likelihood estimates for this model with Gaussian noise have the asymptotic minimax property with maximization over the entire range of the parameter, .