On the asymptotic normality of the R-estimators of the slope parameters of simple linear regression models with positively dependent errors

The purpose of this paper is to prove the asymptotic normality of the rank estimator of the slope parameter of a simple linear regression model with stationary associated errors. This result follows from a uniform linearity property for a linear rank statistics that we establish under general conditions on the dependence of the errors. We prove also a tightness criterion for weighted empirical process constructed from associated triangular arrays. This criterion is needed for the proofs which are based on that of Koul (1977) and of Louhichi (2000).