Statistics and Probability African Society Editions

Chapter 21. Strong limits related to the oscillation modulus of the empirical process based on the k-spacing process

Gane Samb LO

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Abstract

Recently, several strong limit theorems for the oscillation moduli of the empirical process have been given in the iid-case. We show that, with very slight differences, those strong results are also obtained for some representation of the reduced empirical process based on the (nonoverlapping) k-spacings generated by a sequence of independent random variables (rv’s) uniformly distributed on $(0, 1)$. This yields weak limits for the mentioned process. Our study includes the case where the step $k$ is unbounded. The results are mainly derived from several properties concerning the increments of gamma functions with parameters $k$ and one.

Chapter information

Source
Hamet Seydi, Gane Samb Lo, Aboubakary Diakhaby, eds., A Collection of Papers in Mathematics and Related Sciences, a Festschrift in Honour of the Late Galaye Dia, (Calgary, Alberta, 2018), 387-411

Dates
First available in Project Euclid: 26 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.spaseds/1569509481

Digital Object Identifier
doi:10.16929/sbs/2018.100-04-04

Subjects
Primary: 60G30: Continuity and singularity of induced measures 60F15: Strong theorems 60B10: Convergence of probability measures

Keywords
oscillation mudulus empirical processes increments of functions law of the iterated logarithm order statistics

Citation

LO, Gane Samb. Chapter 21. Strong limits related to the oscillation modulus of the empirical process based on the k-spacing process. A Collection of Papers in Mathematics and Related Sciences, 387--411, Statistics and Probability African Society, Calgary, Alberta, 2018. doi:10.16929/sbs/2018.100-04-04. https://projecteuclid.org/euclid.spaseds/1569509481


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