A new algorithm for fixed design regression and denoising

Abstract : In this paper, we present a new algorithm to estimate a regression func- tion in a fixed design regression model, by piecewise (standard and trigonometric) polynomials computed with an automatic choice of the knots of the subdivision and of the degrees of the polynomials on each sub-interval. First we give the theoretical background underlying the method: the theoretical performances of our penalized least-squares estimator are based on non-asymptotic evaluations of a mean-square type risk. Then we explain how the algorithm is built and possibly accelerated (to face the case when the number of observations is great), how the penalty term is cho- sen and why it contains some constants requiring an empirical calibration. Lastly, a comparison with some well-known or recent wavelet methods is made: this brings out that our algorithm behaves in a very competitive way in term of denoising and of compression.
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Annals of the Institute of Statistical Mathematics, Springer Verlag, 2004, 56 (3), pp.449-473
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Fabienne Comte, Yves Rozenholc. A new algorithm for fixed design regression and denoising. Annals of the Institute of Statistical Mathematics, Springer Verlag, 2004, 56 (3), pp.449-473. 〈hal-00748959〉

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