### 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 language | English |
---|---|

Pages (from-to) | 53 - 79 |

Number of pages | 27 |

Journal | Journal of Statistical Planning and Inference |

Volume | 25 |

Publication status | Published - 1989 |

## Fingerprint Dive into the research topics of 'Some stochastic inequalities and asymptotic normality of serial rank statistics in general linear processes'. Together they form a unique fingerprint.

## Cite this

Nieuwenhuis, G., & Ruymgaart, F. H. (1989). Some stochastic inequalities and asymptotic normality of serial rank statistics in general linear processes.

*Journal of Statistical Planning and Inference*,*25*, 53 - 79.