ON THE AVERAGED STOCHASTIC-APPROXIMATION FOR LINEAR-REGRESSION

For a linear regression function the average of stochastic approximati on with constant gain is considered. In case of ergodic observations a lmost sure convergence is proved, where the limit is biased with small bias for small gain. For independent and identically distributed obse rvations and also under martingale and mixing assumptions, asymptotic normality with (n(-1/2))-convergence order is obtained. In the marting ale case the asymptotic covariance matrix is close to the optimum one if the gain is small.