AVERAGE DENSITY ESTIMATORS: EFFICIENCY AND BOOTSTRAP CONSISTENCY

This paper highlights a tension between semiparametric efficiency and bootstrap consistency in the context of canonical estimation problem, namely problem estimating average density. It is shown that although simple plug-in estimators suffer from bias problems preventing them achieving under minimal smoothness conditions, nonparametric automatically corrects for this that, as result, these seemingly inferior achieve conditions. In contrast, several “debiased” conditions do not those same