Bahadur-Kiefer-Type Processes

Paul Deheuvels; David M. Mason

doi:10.1214/aop/1176990852

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Home > Journals > Ann. Probab. > Volume 18 > Issue 2 > Article

April, 1990 Bahadur-Kiefer-Type Processes

Paul Deheuvels, David M. Mason

Ann. Probab. 18(2): 669-697 (April, 1990). DOI: 10.1214/aop/1176990852

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Abstract

We establish strong and weak laws for Bahadur-Kiefer-type processes of the form $e_n + i_n$, where $i_n$ denotes the inverse of $e_n$. In particular, we provide a proof for the strong version of Theorem 1A of Kiefer (1970), together with similar results for renewal and partial sum processes.

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Paul Deheuvels. David M. Mason. "Bahadur-Kiefer-Type Processes." Ann. Probab. 18 (2) 669 - 697, April, 1990. https://doi.org/10.1214/aop/1176990852

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Published: April, 1990

First available in Project Euclid: 19 April 2007

zbMATH: 0712.60028

MathSciNet: MR1055427

Digital Object Identifier: 10.1214/aop/1176990852

Subjects:

Primary: 60F15

Secondary: 60F05 , 60F17 , 62G30

Keywords: Bahadur representation , empirical and quantile processes , order statistics , partial sums and renewal processes , strong laws , weak laws , weighted processes

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