Interpolation methods for nonlinear wavelet regression with irregularly spaced design

Research Report SRR95-042

Interpolation methods for nonlinear wavelet regression with irregularly spaced design

Peter Hall and Berwin A. Turlach

Abstract: We suggest and discuss interpolation methods that enable nonlinear wavelet estimators to be employed with stochastic design, or non-dyadic regular design, in problems of nonparametric regression. This approach allows relatively rapid computation, involving dyadic approximations to wavelet-after-interpolation techniques. New types of interpolation are described, enabling first-order variance reduction at the expense of second-order increases in bias. The effect of interpolation on threshold choice is addressed, and appropriate thresholds are suggested for error distributions with as few as four finite moments. A concise account of mean squared error properties is given for interpolation-based wavelet estimators applied to piecewise-smooth functions.

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