Due to vagueness in the definition of robustness, there has been no natural transition between robust and nonparametric parameter estimators. In this work, qualitative ideas first expressed by Hampel [1] are extended in an effort to present a theory that unifies the nonparametric and robust concepts. Robustness is definied in a precise mathematical way that transists to nonparametricness naturally. As a result, some general constructive characteristics of robust estimators are studied.