Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1154744 | Statistics & Probability Letters | 2007 | 14 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Anestis Antoniadis, Jéremie Bigot, Irène Gijbels,