Wavelet kernel penalized estimation for non-equispaced design regression

    Authors

    U. Amato; A. Antoniadis;M. Pensky

    Comments

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    Abbreviated Journal Title

    Stat. Comput.

    Keywords

    reproducing kernel; wavelet decomposition; penalization; Besov spaces; smoothing splines ANOVA; entropy; SMOOTHING SPLINE ANOVA; BESOV-SPACES; NOISY DATA; SHRINKAGE; REGULARIZATION; INTERPOLATION; SERIES; Computer Science, Theory & Methods; Statistics & Probability

    Abstract

    The paper considers regression problems with univariate design points. The design points are irregular and no assumptions on their distribution are imposed. The regression function is retrieved by a wavelet based reproducing kernel Hilbert space (RKHS) technique with the penalty equal to the sum of blockwise RKHS norms. In order to simplify numerical optimization, the problem is replaced by an equivalent quadratic minimization problem with an additional penalty term. The computational algorithm is described in detail and is implemented with both the sets of simulated and real data. Comparison with existing methods showed that the technique suggested in the paper does not oversmooth the function and is superior in terms of the mean squared error. It is also demonstrated that under additional assumptions on design points the method achieves asymptotic optimality in a wide range of Besov spaces.

    Journal Title

    Statistics and Computing

    Volume

    16

    Issue/Number

    1

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    37

    Last Page

    55

    WOS Identifier

    WOS:000235674500004

    ISSN

    0960-3174

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