Infinite order cross-validated local polynomial regression

Infinite Order Cross-validated Local Polynomial Regression

Many practical problems require nonparametric estimates of regression functions, and local polynomial regression has emerged as a leading approach. In applied settings practitioners often adopt either the local constant or local linear variants, or choose the order of the local polynomial to be slightly greater than the order of the maximum derivative estimate required. But such ad hoc determin...

Local Polynomial Regression

Local Polynomial Regression and SIMEX

This paper introduces a new local polynomial estimator and develops supporting asymptotic theory for non-parametric regression in the presence of covariate measurement error. We address the measurement error with Cook and Stefanski’s simulation-extrapolation (SIMEX) algorithm. Our method improves on previous local polynomial estimators for this problem by (1) using a bandwidth selection procedu...

Local Polynomial Regression and Its Applicationsin

Nonparametric regression estimates a conditional expectation of a response given a predictor variable without requiring parametric assumptions about this conditional expectation. There are many methods of nonparametric regression including kernel estimation, smoothing splines, regression splines, and orthogonal series. Local regression ts parametric models locally by using kernel weights. Local...

Ridging Methods in Local Polynomial Regression

B. Seifert Th. Gasser University of Zurich Department of Biostatistics Sumatrastrasse 30 CH{8006 Z urich, Switzerland Abstract When estimating a regression function r or its th derivative, local polynomials are an attractive choice due to their exibility and asymptotic performance. Seifert & Gasser (1996) proposed local polynomial ridging to overcome problems of local polynomials with variance...