We investigate the extension of binning methodology to fast computation of several auxiliary quantities that arise in local polynomial smoothing. Examples include degrees of freedom measures, cross-validation functions, variance estimates and exact measures of error. It is shown that the computational eeort required for such approximations is of the same order of magnitude as that required for ...

Modal local polynomial regression uses double kernel as the loss function to gain some robustness in the nonparametric regression. Current researches use the standard normal density function as the weight function to down-weigh the influences from the outliers. This paper extends the standard normal weight function to a general class weight functions. All the theoretical properties found by usi...

We reveal the phenomenon that ”naive” multivariate local polynomial regression can adapt to local smooth lower dimensional structure in the sense that it achieves the optimal convergence rate for nonparametric estimation of regression functions belonging to a Sobolev space when the predictor variables live on or close to a lower dimensional manifold.

Local polynomial regression (Fan & Gijbels, 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this paper, we significantly accelerate the computation of local polynomial estimates ...

This paper discusses key results from the literature in the field of local polynomial regression. Local polynomial regression (LPR) is a nonparametric technique for smoothing scatter plots and modeling functions. For each point, x0, a low-order polynomial WLS regression is fit using only points in some “neighborhood” of x0. The result is a smooth function over the support of the data. LPR has g...

Local polynomial smoothers recently received much attention in the literature, owing to their optimality properties (Fan, 1993). However, Seifert and Gasser (1996a; 1996b) showed that in finite samples these smoothers may suffer problems arising from data sparseness. To overcome this problem they suggest a modification based on ridge regression ideas. In this paper we shall describe another app...

We present a fully automated framework to estimate derivatives nonparametrically without estimating the regression function. Derivative estimation plays an important role in the exploration of structures in curves (jump detection and discontinuities), comparison of regression curves, analysis of human growth data, etc. Hence, the study of estimating derivatives is equally important as regressio...