Kernel-Based Semiparametric Estimators: Small Bandwidth Asymptotics and Bootstrap Consistency

Matias D. Cattaneo, Michael Jansson

Research output: Contribution to journalArticle

13 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)955-995
Number of pages41
JournalEconometrica
Volume86
Issue number3
DOIs
StatePublished - May 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

Keywords

  • Semiparametrics
  • bootstrapping
  • robust inference
  • small bandwidth asymptotics

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