Title

On Non-Equally Spaced Wavelet Regression

Keywords

Irregular design; NES regression; Nonparametric statistical procedures; Projection estimators; Wavelets

Abstract

Wavelet-based regression analysis is widely used mostly for equally-spaced designs. For such designs wavelets are superior to other traditional orthonormal bases because of their versatility and ability to parsimoniously describe irregular functions. If the regression design is random, an automatic solution is not available. For such non equispaced designs we propose an estimator that is a projection onto a multiresolution subspace in an associated multiresolution analysis. For defining scaling empirical coefficients in the proposed wavelet series estimator our method utilizes a probabilistic model on the design of independent variables. The paper deals with theoretical aspects of the estimator, in particular MSE convergence rates.

Publication Date

12-1-2001

Publication Title

Annals of the Institute of Statistical Mathematics

Volume

53

Issue

4

Number of Pages

681-690

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1023/A:1014640632666

Socpus ID

6644226793 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/6644226793

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