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

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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Rank Statistics
Linear Process
Asymptotic Normality
Random variables
Statistics
Serial Dependence
Strongly Mixing
Estimator
Lyapunov Theorem
Mixing Processes
I.i.d. Random Variables
Empirical Process
Limit Theorems
Truncation
Serials
Asymptotic normality
Serial dependence
Empirical process
Limit theorems

Cite this

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title = "Some stochastic inequalities and asymptotic normality of serial rank statistics in general linear processes",
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.",
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pages = "53 -- 79",
journal = "Journal of Statistical Planning and Inference",
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Some stochastic inequalities and asymptotic normality of serial rank statistics in general linear processes. / Nieuwenhuis, G.; Ruymgaart, F.H.

In: Journal of Statistical Planning and Inference, Vol. 25, 1989, p. 53 - 79.

Research output: Contribution to journalArticleScientificpeer-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 -