The Annals of Statistics

Interpolation methods for nonlinear wavelet regression with irregularly spaced design

Peter Hall and Berwin A. Turlach

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362378

Digital Object Identifier
doi:10.1214/aos/1069362378

Mathematical Reviews number (MathSciNet)
MR1474074

Zentralblatt MATH identifier
0881.62044

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1069362378


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