Smoothing noisy data with tapered coiflets series

This paper is concerned with an orthogonal wavelet series estimator of an unknown smooth regression function observed with noise on a bounded interval. A penalized least-squares approach is adopted and our method uses the specific asymptotic interpolating properties of the wavelet approximation generated by a particular wavelet basis, Daubechie's coiflets. A simple procedure is described to estimate the smoothing parameter of the penalizing functional and conditions are given for the estimator to attain optimal convergence rates in the integrated mean square sense as the sample size increases to infinity. The results are illustrated with simulated and real examples and a comparison with other non-parametric smoothers is made.