On the Bahadur representation of sample quantiles for score functionals

TL;DR

This paper derives the Bahadur representation for sample quantiles of stabilizing score functionals in stochastic geometry, analyzing their fluctuations and applying results to trimmed and Winsorized means, including a law of the iterated logarithm.

Contribution

It introduces the Bahadur representation for score functionals derived from Poisson processes, advancing understanding of their quantile fluctuations.

Findings

Bahadur representation established for score functionals

Law of the iterated logarithm proved for sample quantiles

Results applied to trimmed and Winsorized means

Abstract

We establish the Bahadur representation of sample quantiles for stabilizing score functionals in stochastic geometry and study local fluctuations of the corresponding empirical distribution function. The scores are obtained from a Poisson process. We apply the results to trimmed and Winsorized means of the score functionals and establish a law of the iterated logarithm for the sample quantiles of the scores.