### Abstract

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 |

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*Journal of Statistical Planning and Inference*,

*25*, 53 - 79.

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

**Some stochastic inequalities and asymptotic normality of serial rank statistics in general linear processes.** / Nieuwenhuis, G.; Ruymgaart, F.H.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Some stochastic inequalities and asymptotic normality of serial rank statistics in general linear processes

AU - Nieuwenhuis, G.

AU - Ruymgaart, F.H.

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

M3 - Article

VL - 25

SP - 53

EP - 79

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

ER -