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Digital Object Identifier (DOI) 10.1007/s004400000048 Probab. Theory Relat. Fields 117, 133144 (2000) c Springer-Verlag 2000
 

Summary: Digital Object Identifier (DOI) 10.1007/s004400000048
Probab. Theory Relat. Fields 117, 133144 (2000) c Springer-Verlag 2000
F. Abramovich T. Sapatinas B.W. Silverman
Stochastic expansions in an overcomplete
wavelet dictionary
Received: 21 September 1998 / Revised version: 20 August 1999 /
Published online: 30 March 2000
Abstract. We consider random functions defined in terms of members of an overcomplete
wavelet dictionary. The function is modelled as a sum of wavelet components at arbitrary po-
sitions and scales where the locations of the wavelet components and the magnitudes of their
coefficients are chosen with respect to a marked Poisson process model. The relationships
between the parameters of the model and the parameters of those Besov spaces within which
realizations will fall are investigated. The models allow functions with specified regularity
properties to be generated. They can potentially be used as priors in a Bayesian approach
to curve estimation, extending current standard wavelet methods to be free from the dyadic
positions and scales of the basis functions.
1. Introduction
1.1. Background
Wavelets have recently been of great interest in various statistical areas such as
nonparametric regression, density estimation, inverse problems, change point prob-

  

Source: Abramovich, Felix - School of Mathematical Sciences, Tel Aviv University
Sapatinas, Theofanis - Department of Mathematics and Statistics, University of Cyprus

 

Collections: Mathematics