Title: Komlós-Major-Tusnády approximations to increments of uniform empirical processes,
Abstract: The well-known Komlós-Major-Tusnády 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.