Open Access
VOL. 1 | 2018 Chapter 21. Strong limits related to the oscillation modulus of the empirical process based on the k-spacing process
Gane Samb LO

Editor(s) Hamet SEYDI, Gane Samb LO, Aboubakary DIAKHABY


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.


Published: 1 January 2018
First available in Project Euclid: 26 September 2019

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

Primary: 60B10 , 60F15 , 60G30

Keywords: Empirical processes , increments of functions , Law of the iterated logarithm , order statistics , oscillation mudulus

Rights: Copyright © 2018 The Statistics and Probability African Society

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