Convolution and interpolation competitors with local polynomial smoothing

Research Report SRR95-037

Convolution and interpolation competitors with local polynomial smoothing

Peter Hall and Berwin A. Turlach

Abstract: Local polynomial smoothing enjoys a variety of very attractive features. It is often viewed as superior to convolution and interpolation methods, which offer greater numerical stability but inferior theoretical performance. In this paper we show that modifications to convolution and interpolation techniques produce effective competitors with local polynomial smoothing, enjoying similar bias, variance and mean squared error properties but without the downside of numerical instability. The methods suggested here may be employed as the basis for empirical wavelet transforms of ungridded data.

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