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

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  • Cattaneo, Matias D.
  • Farrell, Max H.

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.

Suggested Citation

  • Cattaneo, Matias D. & Farrell, Max H., 2013. "Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators," Journal of Econometrics, Elsevier, vol. 174(2), pages 127-143.
    • Handle: RePEc:eee:econom:v:174:y:2013:i:2:p:127-143
    DOI: 10.1016/j.jeconom.2013.02.002
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    References listed on IDEAS

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    More about this item

    Keywords

    Nonparametric estimation; Partitioning; Subclassification; Convergence rates; Bahadur representation; Asymptotic normality;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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