Asymptotic uniform linearity of some robust statistics under exponentially subordinated strongly dependent models

In this paper, we discuss an asymptotic distributional theory of three broad classes of robust estimators of the regression parameter namely, L-, M- and R-estimators in a linear regression model when the errors are generated by an exponentially subordinated strongly dependent process. The results are obtained as a consequence of an asymptotic uniform Taylor-type expansion of certain randomly weighted empirical processes. The limiting distributions of the estimators are nonnormal and depend on the first nonzero index of the Laguerre polynomial expansion of a class of indicator functions of the error random variables.