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

G. Nieuwenhuis, F.H. Ruymgaart

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)53 - 79
Number of pages27
JournalJournal of Statistical Planning and Inference
Volume25
Publication statusPublished - 1989

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