Enhancing convolution and interpolation methods for nonparametric regression

Abstract

Following earlier work of Jones, Davies & Park (1994) we develop estimators based on convolution and interpolation methods, with the aim of reducing their variance and making them competitive with local linear smoothers. We argue that the classic convolution and interpolation approaches due to Gasser & Müller (1979) and Clark (1977) exhibit inflated variance on account of the relatively high variability of weights used in their construction. We show that, by convolving or interpolating over only a small additional number of design points, variance is reduced by a constant factor. Theoretical and numerical properties are summarised.