Annals of Statistics

Interpolation methods for nonlinear wavelet regression with irregularly spaced design

Peter Hall and Berwin A. Turlach

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We introduce interpolation methods that enable nonlinear wavelet estimators to be employed with stochastic design, or nondyadic 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.

Article information

Ann. Statist., Volume 25, Number 5 (1997), 1912-1925.

First available in Project Euclid: 20 November 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation
Secondary: 62G30: Order statistics; empirical distribution functions

Bias mean squared error nonparametric regression piecewise smooth stochastic design threshold variance


Hall, Peter; Turlach, Berwin A. Interpolation methods for nonlinear wavelet regression with irregularly spaced design. Ann. Statist. 25 (1997), no. 5, 1912--1925. doi:10.1214/aos/1069362378.

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