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.

本文通过引入经验过程方法，提出了超范数损失中非参数函数小波估计的均匀强一致性率。对解释变量的紧凑支持假设常用于非参数回归分析。在文章中，我们考虑了小波估计分析，没有对解释变量的支持的兼容性做任何​​假设。The optimal uniform convergence rates of the wavelet estimators are achieved by suitably choosing resolution level. 这些结果对于非参数信号恢复和分析的小波理论很有用。