Koml\'os-Major-Tusn\'ady approximations to increments of uniform empirical processes

TL;DR

This paper uses Komlós-Major-Tusnádý inequalities to achieve Gaussian approximations for weighted increments of uniform empirical and quantile processes, with applications to extreme value statistics in censored data.

Contribution

It introduces a novel application of KMT inequalities to approximate increments of empirical processes, enabling precise rates and applications to censored data analysis.

Findings

Established Gaussian approximation rates for empirical process increments.

Applied results to extreme value statistics in censored data.

Provided theoretical bounds with potential practical implications.

Abstract

The well-known Koml\'os-Major-Tusn\'ady inequalities [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] provide sharp inequalities to partial sums of iid standard exponential random variables by a sequence of standard Brownian motions. In this paper, we employ these results to establish Gaussian approximations to weighted increments of uniform empirical and quantile processes. This approach provides rates to the approximations which, among others, have direct applications to statistics of extreme values for randomly censored data.