1. Penalized wavelet monotone regression
- Author
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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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