A general result on the uniform in bandwidth consistency of kernel-type function estimators

We develop a general theorem to prove the uniform in bandwidth consistency of kernel-type function estimators. This method unifies the approaches in some other recent papers. We show how to apply our results to kernel distribution function estimators and the smoothed empirical process. The results are applicable to establish strong uniform consistency of data-driven bandwidth kernel-type function estimators. Copyright Sociedad de Estadística e Investigación Operativa 2011