Uniform convergence rates for wavelet curve estimation in sup-norm loss

Abstract

This paper presents the rates of uniform strong consistency of wavelet estimation for nonparametric function in sup-norm loss by introducing an empirical process approach. A compact support assumption on the explanatory variable is commonly used in nonparametric regression analysis. In the article, we consider the wavelet estimation analysis without any assumption on the compacity of the support of the explanatory variable. The optimal uniform convergence rates of the wavelet estimators are achieved by suitably choosing resolution level. These results are useful for wavelet theory on nonparametric signal recovery and analysis.