Dependent Asymptotic Properties Of The S-estimate Of The Error Under

This thesis consists of three parts in which the asymptotics of S-estimators in different models with different dependent error variables are investigated.In part one, the asymptotic properties of S-estimators in the linear regression model with mixing error terms are obtained. It turns out that S-estimators are strong consistent and asymptotically normal with a similar variance-covariance structure as in the i.i.d. case. We majorally study two cases in which the error terms {e_i, i = 1,2,···, n} are α mixing sequence and φ mixing sequence, respectively.In part two, we investigate the asymptotic properties of S-estimators in the linear regression model with negatively associated or positively associated error terms. It turns out that under some suitable conditions those properties of S-estimators also hold.A general form of S-estimation is proposed and some asymptotics are investigated in part three. The model covers all linear and nonlinear regression models, AR time series, EIVR models, etc. as its special cases.