Limit properties of the monotone rearrangement for density and regression function estimation
The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and Po ́lya as a sorting device for functions. As- suming that x is a monotone function and that an estimate xn of x is given, consider the monotone rearrangement xˆn of xn. This new estimator is shown to be uniformly consistent. Under suitable as- sumptions, pointwise limit distribution results for xˆn are obtained. The fra
