The sequential estimation in stochastic regression model with random coefficients

Abstract

This paper considers the problem of sequential point estimation and fixed accuracy confidence set procedures of parameters in a stochastic regression model with random coefficients. The sequential estimator proposed is based on the least-squares estimator and is shown to be risk efficient as the cost of estimation error tends to infinity. Furthermore, the proposed procedure for fixed-width confidence set is shown to be both asymptotically consistent and asymptotically efficient as the width approaches zero.