Processus empiriques des rapports de m-espacements uniformes disjoints (Non-overlapping uniform m-spacings-ratio empirical processes)

2011/09/29 by Moïse Jérémie, Jérémie, Moïse
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1109.6611

openalex publication_date 2011/09/29 · arxiv created 2012/11/07 · arxiv updated 2012/11/09 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We consider an empirical process based upon ratio of selected pair of the non-overlapping m-spacings generated by independent samples of arbitrary sizes. As a main result, we show that when both samples are uniformly distributed on intervals of equal lengths, this empirical process converges to a mean-centered Brownian bridge of the form (B∘ H_m)_C(v)=B(H_m(v))-2(2m+1)C ((2m-1)!)/(m((m-1)!)²)(v(1-v))^m∫₀¹B(H_m(s))\ud s, for 0≤ v≤ 1, where B(.) denotes a Brownian bridge, H_m, the distribution function of the Beta distribution with parameters m and m, and C, a constant.

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