Interpolation methods for nonlinear wavelet regression with irregularly spaced design

Peter Hall, Berwin A. Turlach

Research output: Contribution to journalArticlepeer-review

62 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1912-1925
Number of pages14
JournalAnnals of Statistics
Issue number5
Publication statusPublished - Oct 1997
Externally publishedYes


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