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Statistica Sinica 7(1997), 1171-1180


M. C. Jones

Open University

Abstract: There has been much justifiable recent interest in local polynomial regression, and in particular in its local linear special case. Local linear regression has advantages in terms of desirable theoretical properties both in the interior and near the boundaries of the region of interest. For implementation, binning is useful. In this paper, we describe a variation on local linear regression which can be considered an alternative binning thereof. We show that existing and novel methods are almost indistinguishable. The point of the paper is not to extol the virtues of the new version over the old, but rather (i) to show that the good properties of local linear regression can be achieved in more than one way, and (ii) to elucidate close links between local linear regression and other kernel smoothing methods. The latter include, most closely, a boundary corrected `naive' kernel estimator and a recent proposal of Wu and Chu (1992), as well as binned Nadaraya-Watson estimators and methods for binomial regression.

Key words and phrases: Binning, boundary correction, kernel smoothing, nonparametric regression.

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