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2 results on '"Wavelet nonparametric regression"'

1. Penalized wavelet monotone regression

Author

Antoniadis, Anestis, Bigot, Jéremie, and Gijbels, Irène

Subjects
*REGRESSION analysis, *MATHEMATICAL optimization, *NUMERICAL analysis, *CURVE fitting
Abstract

Abstract: In this paper we focus on nonparametric estimation of a constrained regression function using penalized wavelet regression techniques. This results into a convex optimization problem under linear constraints. Necessary and sufficient conditions for existence of a unique solution are discussed. The estimator is easily obtained via the dual formulation of the optimization problem. In particular we investigate a penalized wavelet monotone regression estimator. We establish the rate of convergence of this estimator, and illustrate its finite sample performance via a simulation study. We also compare its performance with that of a recently proposed constrained estimator. An illustration to some real data is given. [Copyright &y& Elsevier]

Published
2007
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2. Penalized wavelet monotone regression

Author

Anestis Antoniadis, Jérémie Bigot, Irène Gijbels, Statistique et Modélisation Stochatisque (SMS), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Leuven Statistics Research Centre (LStat), Catholic University of Leuven - Katholieke Universiteit Leuven (KU Leuven), Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Université Joseph Fourier Grenoble 1 - UJF (FRANCE), Katholieke Universiteit Leuven - KU LEUVEN (BELGIUM), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Splines, Statistics and Probability, Monotonicity, Statistics::Theory, Mathematical optimization, Optimization problem, Wavelets, 01 natural sciences, Statistics::Machine Learning, 010104 statistics & probability, Minimum-variance unbiased estimator, Wavelet, Constrained curve fitting, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 0502 economics and business, Statistics::Methodology, 0101 mathematics, Wavelet nonparametric regression, 050205 econometrics, Mathematics, Wavelet thresholding, 05 social sciences, Constrained optimization, Estimator, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], MSC: 62G07, 65Dxx, Nonparametric regression, Besov spaces, Convex optimization, Statistiques, Statistics, Probability and Uncertainty, Minimax estimator
Abstract

International audience; In this paper we focus on nonparametric estimation of a constrained regression function using penalized wavelet regression techniques. This results into a convex optimization problem under linear constraints. Necessary and sufficient conditions for existence of a unique solution are discussed. The estimator is easily obtained via the dual formulation of the optimization problem. In particular we investigate a penalized wavelet monotone regression estimator. We establish the rate of convergence of this estimator, and illustrate its finite sample performance via a simulation study. We also compare its performance with that of a recently proposed constrained estimator. An illustration to some real data is given.

Published
2007

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