## 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

#### 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

#### 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