AVERAGE DENSITY ESTIMATORS: EFFICIENCY AND BOOTSTRAP CONSISTENCY

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...

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Bibliographic Details
Published inEconometric theory Vol. 38; no. 6; pp. 1140 - 1174
Main Authors Cattaneo, Matias D., Jansson, Michael
Format Journal Article
LanguageEnglish
Published New York, USA Cambridge University Press 01.12.2022
Subjects
Bias
Density
Econometrics
Economic theory
Efficiency
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Summary: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.
ISSN:0266-4666
1469-4360
DOI:10.1017/S0266466621000530