The Annals of Statistics
- Ann. Statist.
- Volume 25, Number 5 (1997), 1912-1925.
Interpolation methods for nonlinear wavelet regression with irregularly spaced design
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.
Ann. Statist., Volume 25, Number 5 (1997), 1912-1925.
First available in Project Euclid: 20 November 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G07: Density estimation
Secondary: 62G30: Order statistics; empirical distribution functions
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