A NEW CLASS OF CONSISTENT ESTIMATORS FOR STOCHASTIC LINEAR REGRESSIVEMODELS

In this paper we propose a new approach for estimating the unknown par ameter in the stochastic linear regressive model with stationary ergod ic sequence of covariates. Under mild conditions on the joint distribu tion of the covariate and the error, the estimator constructed is show n to be strongly consistent in two important special cases: (1) The se quence of (variate, covariate) is independent identically distributed (i.i.d.), and (2) the sequence of variates is a stationary autoregress ive series. the asymptotical normality is also discussed under more as sumptions on the distribution of the covariate. (C) 1997 Academic Pres s.