@article{4dee4cead425440d85a2078390549098,
title = "AVERAGE DENSITY ESTIMATORS: EFFICIENCY AND BOOTSTRAP CONSISTENCY",
abstract = "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.",
author = "Cattaneo, {Matias D.} and Michael Jansson",
note = "Funding Information: For comments and suggestions, we are grateful to the Co-Editor, two referees, and seminar participants at the Cowles Foundation conference celebrating Peter Phillips{\textquoteright}s 40 years at Yale, the 2018 LAMES conference, the 2019 CIREQ Montreal Econometrics Conference, ITAM, University of North Carolina, Princeton University, UC Santa Barbara, and Oxford University. Cattaneo gratefully acknowledges financial support from the National Science Foundation through grants SES-1459931 and SES-1947805, and Jansson gratefully acknowledges financial support from the National Science Foundation through grants SES-1459967 and SES-1947662, and the research support of CREATES (funded by the Danish National Research Foundation under grant no. DNRF78). Publisher Copyright: {\textcopyright} The Author(s), 2021. Published by Cambridge University Press.",
year = "2022",
month = dec,
day = "23",
doi = "10.1017/S0266466621000530",
language = "English (US)",
volume = "38",
pages = "1140--1174",
journal = "Econometric Theory",
issn = "0266-4666",
publisher = "Cambridge University Press",
number = "6",
}