Annals of the Institute of Statistical Mathematics vol:59 issue:2 pages:235-272
In this paper a nonparametric method to estimate the regression by considering the possibility of preserving the jump points of the regression curve and providing smooth estimates at its points of continuity is introduced and analyzed. According to the weighted residual mean squares, one of three possible estimates is chosen at each point. The local linear estimates at each point x consider only the left data points, only the right data points or both in a neighbourhood of x.
The consistency of the estimator is shown and illustrated by means of some simulations. Some empirical comparisons with previous methods and a case-study concerning penny thickness are also included.