Cai, T. (2002) On Adaptive Wavelet Estimation of a Derivative and Other Related Linear Inverse Problems. Journal of Statistical Planning and Inference, 108, 329-349.

has been cited by the following article:

• TITLE: Estimation of Regression Function for Nonequispaced Samples Based on Warped Wavelets

  AUTHORS: Nargess Hosseinioun

  KEYWORDS: Dependent Sequence, Nonparametric Regression, Random Design, Warped Wavelet Basis

  JOURNAL NAME: Open Journal of Statistics, Vol.6 No.1, February 23, 2016

  ABSTRACT: We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warped wavelet basis. We investigate the properties of this new basis and evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error under different dependence structures. We prove that it attains a sharp rate of convergence for a wide class of unknown regression functions.