Dragi Anevski, Göteborg University,

Hardy-Littlewood-Polya's monotone rearrangement algorithm.
(joint work with Anne-Luare  Fougeres, Paris)

Abstract

Sorting a discrete set of points is an elementary operation. The
order statistic describes the probabilistic behaviour of the sorted
set of points. The "sorting" of an e.g. continuous function is given
by the Hardy-Littlewood-Polya monotone rearrangement algorithm. We
apply the algorith to the monotonization of estimates of density and
regression functions, and state the limit distributions under general
dependence assumptions for the obtained estimates.