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

2014/06/28 by Gane Samb Lô, Lo, Gane Samb
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Approximation and Integration #Methodology (stat.ME) #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1406.7434

openalex publication_date 2014/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (non-overlapping) 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.

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