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

TL;DR

This paper extends strong approximation results and functional limit laws for non-overlapping k-spacings processes, generalizing previous work and applying invariance principles to characterize their limit behaviors.

Contribution

It provides new strong approximation results and generalizes existing limit laws for increments of k-spacings quantile processes.

Findings

Established strong approximations for non-overlapping k-spacings processes.

Generalized limit laws for increments of k-spacings quantile processes.

Characterized the limit behavior of functionals of these processes.

Abstract

The first 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.