Dragi Anevsk 

The monotone rearrangement algorithm

Abstract

Hardy, Littlewood and Polya presented the monotone rearrangement algorithm
as a tool in analysis in their classic book "Inequalities". The algorithm
can be seen as a sorting device for real valued functions on (a subset of)
the real line. We propose to use the algorithm as a general tool for
nonparametric inference under order restrictions. We derive limit
distributions for the obtained estimators, that hold for various dependence
situations such as i.i.d. data, weakly dependent mixing data and long range
dependent data. Two applications are given, to regression function and
density function estimation under monotonicity.