On non-equally spaced wavelet regression

    Authors

    M. Pensky;B. Vidakovic

    Abbreviated Journal Title

    Ann. Inst. Stat. Math.

    Keywords

    irregular design; NES regression; nonparametric statistical procedures; projection estimators; wavelets; CURVE ESTIMATION; SHRINKAGE; DESIGN; Statistics & Probability

    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.

    Journal Title

    Annals of the Institute of Statistical Mathematics

    Volume

    53

    Issue/Number

    4

    Publication Date

    1-1-2001

    Document Type

    Article

    Language

    English

    First Page

    681

    Last Page

    690

    WOS Identifier

    WOS:000173369300002

    ISSN

    0020-3157

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