Estimators with Prescribed Precision in Stochastic Regression Models

This paper presents stopping rules and associated estimators, with prescribed mean squared errors, of the regression parameters in stochastic regression models. The construction makes fundamental use of the martingale structure of least squares estimates or their modifications. For one-dimensional regressors, the stopping rules simply stop as soon as the conditional variance of the underlying martingale exceeds some suitably chosen threshold. We show how this idea can be modified for the case of multidimensional stochastic regressors.