Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators

Matias D. Cattaneo, Max H. Farrell

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

This paper studies the asymptotic properties of partitioning estimators of the conditional expectation function and its derivatives. Mean-square and uniform convergence rates are established and shown to be optimal under simple and intuitive conditions. The uniform rate explicitly accounts for the effect of moment assumptions, which is useful in semiparametric inference. A general asymptotic integrated mean-square error approximation is obtained and used to derive an optimal plug-in tuning parameter selector. A uniform Bahadur representation is developed for linear functionals of the estimator. Using this representation, asymptotic normality is established, along with consistency of a standard-error estimator. The finite-sample performance of the partitioning estimator is examined and compared to other nonparametric techniques in an extensive simulation study.

Original languageEnglish (US)
Pages (from-to)127-143
Number of pages17
JournalJournal of Econometrics
Volume174
Issue number2
DOIs
StatePublished - Jun 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

Keywords

  • Asymptotic normality
  • Bahadur representation
  • Convergence rates
  • Nonparametric estimation
  • Partitioning
  • Subclassification

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