Nonparametric regression quantiles obtained by inverting a kernel estimator of the conditional distribution of the response are long established in statistics. Attention has been, however, restricted to ordinary quantiles staying away from the tails of the conditional distribution. The purpose of this paper is to extend their asymptotic theory far enough into the tails. We focus on extremal qua...

The present paper is dealing with optimization problems arising in the context of kernel estimates of a density and a regression function. Kernel estimates are one of the most popular nonparametric functional estimates. These estimates depend on a bandwidth which controls the smoothness of the estimate and on a kernel which plays a role of a weight function. In this paper we concentrate on a ch...

In this paper we propose a simple multistep regression smoother which is constructed in a boosting fashion, by learning the Nadaraya–Watson estimator with L2Boosting. Differently from the usual approach, we do not focus on L2Boosting for ever. Given a kernel smoother as a learner, we explore the boosting capability to build estimators using a finite number of boosting iterations. This approach ...

Instead of using the polygon defined by adjacent vertices to a vertex (called the ball) or its kernel [1], we propose a modified polygon that is easy to compute, convex and an approximation of the kernel. We call this polygon the “quick kernel ball region.” This novel algorithm is presented in details. It is easy to implement and effective in constraining a vertex to remain within its feasible ...