Penalized wavelet monotone regression

Anestis Antoniadis, Jéremie Bigot and Irène Gijbels

Statistics & Probability Letters, 2007, vol. 77, issue 16, 1608-1621

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.

Keywords: Besov; spaces; Constrained; curve; fitting; Monotonicity; Splines; Wavelets; Wavelet; nonparametric; regression; Wavelet; thresholding (search for similar items in EconPapers)
Date: 2007
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