Some stochastic inequalities and asymptotic normality of serial rank statistics in general linear processes

Let Xj=ΣkϵzgkEj−k define a general linear process based on i.i.d. random variables Ej in R. Stochastic inequalities in terms of reduced empirical processes of Xi for i≤n and related (Xi>,Xi+h) are obtained by a truncation argument (cf. Chanda and Ruymgaart (1988)). Then rank estimators of serial dependence are considered which are based on scores, possibly unbounded. Asymptotic normality is established by a proof that involves Lyapunov's limit theorem and may have some independent interest. Even with not strongly mixing linear processes asymptotically normal rank estimators may occur, as shows an example.