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

本文强调了在典型半参数估计问题（即估计平均密度的问题）的背景下，半参数效率与自举一致性之间的紧张关系。结果表明，尽管简单的插件估计器存在偏差问题，阻止它们在最小平滑度条件下实现半参数效率，但非参数引导程序会自动纠正这种偏差，因此，这些看似较差的估计器在最小平滑度下实现引导程序一致性状况。相比之下，几个在最小平滑度条件下实现半参数效率的“去偏”估计器在相同条件下无法实现自举一致性。