Before revision:  We give conditions under which such estimators are consistent, and describe their asymptotic mean squared error properties . Analytic examples illustrate the situations where re-weighting provides a reduction in variance , and a simulation study is conducted to evaluate small sample performance of the proposed estimators .
After revision:  We give conditions under which such estimators are consistent, and describe their asymptotic mean squared error properties of the kernel density and distribution estimators proposed in the paper. A simulation study evaluates the small sample performance of these estimators. Supplements provide analytic examples to illustrate situations where kernel weighting provides a reduction in variance , and a simulation study is conducted to evaluate small sample performance of the proposed estimators .