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October 1997 Interpolation methods for nonlinear wavelet regression with irregularly spaced design
Peter Hall, Berwin A. Turlach
Ann. Statist. 25(5): 1912-1925 (October 1997). DOI: 10.1214/aos/1069362378


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.


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Peter Hall. Berwin A. Turlach. "Interpolation methods for nonlinear wavelet regression with irregularly spaced design." Ann. Statist. 25 (5) 1912 - 1925, October 1997.


Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0881.62044
MathSciNet: MR1474074
Digital Object Identifier: 10.1214/aos/1069362378

Primary: 62G07
Secondary: 62G30

Keywords: bias , mean squared error , Nonparametric regression , piecewise smooth , stochastic design , threshold , variance

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 5 • October 1997
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