A New Class of Consistent Estimators for Stochastic Linear Regressive Models

In this paper we propose a new approach for estimating the unknown parameter in the stochastic linear regressive model with stationary ergodic sequence of covariates. Under mild conditions on the joint distribution of the covariate and the error, the estimator constructed is shown to be strongly consistent in two important special cases: (1) The sequence of (variate, covariate) is independent identically distributed (i.i.d.), and (2) the sequence of variates is a stationary autoregressive series. The asymptotical normality is also discussed under more assumptions on the distribution of the covariate.