Sequential Generlized Least squares Estimator For An Autoressive parameter

Abstract

The paper considers a sequential estimator for the parameter of the first order autoregressive model with unknown noise variance based on the generalized least squares estimator. The estimator has a prescribed mean squared accuracy and is asymptotically normally distributed uniformly in the autoregressive parameter taking values in any compact subset of the real line. The estimator is shown to be asymptotically minimax (in the Hajek-LeCam sense) in a large class of sequential and fixed sample size esti~nation procedures.