Penalized wavelet monotone regression

Anestis Antoniadis (1) , Jérémie Bigot (2) , Irène Gijbels (3)

1 SMS - Statistique et Modélisation Stochatisque
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 LStat - Leuven Statistics Research Centre

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.

Mots clés: Besov spaces; Constrained curve fitting; Monotonicity; Splines; Wavelets; Wavelet nonparametric regression; Wavelet thresholding

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Anestis Antoniadis, Jérémie Bigot, Irène Gijbels. Penalized wavelet monotone regression. Statistics and Probability Letters, 2007, 77 (16), pp.1608-1621. ⟨10.1016/j.spl.2007.03.041⟩. ⟨hal-00397534⟩