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Biometrika 2001 88(3):805-820; doi:10.1093/biomet/88.3.805
© 2001 by Biometrika Trust
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Wavelet shrinkage for natural exponential families with quadratic variance functions

Anestis Antoniadis1 and Theofanis Sapatinas2

1 Laboratoire IMAG-LMC, University Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, Franceanestis.antoniadis{at}imag.fr 2 Department of Mathematics and Statistics, University of Cyprus, P.O.Box 20537, CY 1678 Nicosia, Cyprus. t.sapatinas{at}ucy.ac.cy

We propose a wavelet shrinkage methodology for univariate natural exponential families with quadratic variance functions, covering the Gaussian, Poisson, gamma, binomial, negative binomial and generalised hyperbolic secant distributions.Simulation studies for Poisson and binomial data are used to illustrate the usefulness of the proposed methodology, and comparisons are made with other methods available in the literature. We also present applications to datasets arising from high-energy astrophysics and from epidemiology.

Key Words: Crossvalidation mean squared error; Diagonal shrinkage estimation; Modulation estimator; Natural exponential family; Nonparametric regression; Smoothing; Wavelet shrinkage estimation

Received January 2000. Revised October 2000


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