On the strong approximation and functional limit laws for the increments of the non-overlapping k-spacings processes

Salim Bouzebda (1) , Nabil Nessigha (1)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

The first aim of the present paper, is to establish strong approximations of the uniform non-overlapping k-spacings process extending the results of Aly et al. (1984). Our methods rely on the invariance principle in Mason and van Zwet (1987). The second goal, is to generalize the Dindar (1997) results for the increments of the spacings quantile process to the uniforme non-overlapping k-spacings quantile process. We apply the last result to characterize the limit laws of functionals of the increments k-spacings quantile process.

Mots clés: 60F15; Functional laws of the iterated logarithm; Gaussian processes; Stochastic processes; Quantile processes.; Strong approximations; Quantile processes; Func- tional laws of the iterated logarithm; Quantile processes MSC 2010: 62E20

Domaines: Théorie [stat.TH]; Statistiques [math.ST]

Salim Bouzebda, Nabil Nessigha. On the strong approximation and functional limit laws for the increments of the non-overlapping k-spacings processes. 2020. ⟨hal-00305487v2⟩