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AVERAGE DENSITY ESTIMATORS: EFFICIENCY AND BOOTSTRAP CONSISTENCY

Published online by Cambridge University Press:  23 December 2021

Matias D. Cattaneo  and
Michael Jansson
Matias D. Cattaneo
Affiliation:
Princeton University
Michael Jansson*
Affiliation:
University of California at Berkeley
*
Address correspondence to Michael Jansson, Department of Economics and CREATES, University of California at Berkeley, Berkeley, CA, USA; e-mail: [email protected].
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Abstract

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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.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 6: YALE 2018 CONFERENCE IN HONOR OF PETER C. B. PHILLIPS: PART II , December 2022 , pp. 1140 - 1174
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

For comments and suggestions, we are grateful to the Co-Editor, two referees, and seminar participants at the Cowles Foundation conference celebrating Peter Phillips’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).

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