@article{a06a8633b36f431ca2e8c3ff0e69ec59,
title = "Kernel-Based Semiparametric Estimators: Small Bandwidth Asymptotics and Bootstrap Consistency",
abstract = "This paper develops asymptotic approximations for kernel-based semiparametric estimators under assumptions accommodating slower-than-usual rates of convergence of their nonparametric ingredients. Our first main result is a distributional approximation for semiparametric estimators that differs from existing approximations by accounting for a bias. This bias is nonnegligible in general, and therefore poses a challenge for inference. Our second main result shows that some (but not all) nonparametric bootstrap distributional approximations provide an automatic method of correcting for the bias. Our general theory is illustrated by means of examples and its main finite sample implications are corroborated in a simulation study.",
keywords = "Semiparametrics, bootstrapping, robust inference, small bandwidth asymptotics",
author = "Cattaneo, {Matias D.} and Michael Jansson",
note = "Funding Information: Matias D. Cattaneo: cattaneo@umich.edu Michael Jansson: mjansson@econ.berkeley.edu A previous version of this paper was circulated under the title “Bootstrapping Kernel-Based Semiparamet-ric Estimators.” We thank the handling coeditor, four referees, Stephane Bonhomme, Lutz Kilian, Xinwei Ma, Whitney Newey, Jamie Robins, Adam Rosen, Andres Santos, Azeem Shaikh, Xiaoxia Shi, and seminar participants at Cambridge University, Georgetown University, London School of Economics, Oxford University, Rice University, University of Chicago, University College London, University of Michigan, the 2013 Latin American Meetings of the Econometric Society, and 2014 CEME/NSF Conference on Inference in Nonstandard Problems for comments. The first author gratefully acknowledges financial support from the National Science Foundation (SES 1122994 and SES 1459931). The second author gratefully acknowledges financial support from the National Science Foundation (SES 1124174 and SES 1459967) and the research support of CREATES (funded by the Danish National Research Foundation under Grant no. DNRF78). Publisher Copyright: {\textcopyright} 2018 The Econometric Society",
year = "2018",
month = may,
doi = "10.3982/ECTA12701",
language = "English (US)",
volume = "86",
pages = "955--995",
journal = "Econometrica",
issn = "0012-9682",
publisher = "Wiley-Blackwell",
number = "3",
}