A new algorithm for fixed design regression and denoising |
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Authors: | F Comte Y Rozenholc |
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Institution: | (1) MAP5, UMR CNRS 8145, Université Paris 5, 45 rue des Saints-Pères, 75270 Paris cedex 06, France;(2) LPMA, UMR CNRS 7599, Université Paris VII, 175 rue du Chevaleret, 75013 Paris, France;(3) Université du Maine, Le Mans, France |
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Abstract: | In this paper, we present a new algorithm to estimate a regression function 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 chosen 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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Keywords: | Least-squares regression piecewise polynomials adaptive estimation model selection dynamical programmation algorithm for denoising |
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