SFB 303 Discussion Paper No. A-431

Author: Engel, Joachim, and Alois Kneip
Title: A Remedy for Kernel Regression under Random Design
Abstract: Two common kernel-based methods for non-parametric regression estimation suffer from well-known drawbacks when the design is random. The Gasser-Müller estimator is inadmissible due to its high variance while the Nadaraya-Watson estimator has zero asymptotic efficiency because of poor bias behavior. Under asymptotic considerations, the local linear estimator avoids these two drawbacks of kernel estimators and achieves minimax optimality. However, when based on compact support kernels its finite sample behavior is disappointing because sudden kinks may show up in the estimate. This paper proposes a modification of the kernel estimator, called the binned convolution estimator leading to a method about as fast as WARPING with asymptotic properties identical with those of the local linear estimator.
Keywords: Kernel regression; Local polynomials; Smoothing; Binning; WARPING
JEL-Classification-Number: C14, C13, C15
Creation-Date: February 1994
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