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

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  • Matias D. Cattaneo
  • Michael Jansson

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.

Suggested Citation

  • Matias D. Cattaneo & Michael Jansson, 2018. "Kernel†Based Semiparametric Estimators: Small Bandwidth Asymptotics and Bootstrap Consistency," Econometrica, Econometric Society, vol. 86(3), pages 955-995, May.
    • Handle: RePEc:wly:emetrp:v:86:y:2018:i:3:p:955-995
    DOI: 10.3982/ECTA12701
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    References listed on IDEAS

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    Cited by:

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    2. Yulia Kotlyarova & Marcia M. A. Schafgans & Victoria Zinde-Walsh, 2021. "Rates of Expansions for Functional Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 121-139, December.
    3. Wang, Yulong & Xiao, Zhijie, 2022. "Estimation and inference about tail features with tail censored data," Journal of Econometrics, Elsevier, vol. 230(2), pages 363-387.
    4. Matias D Cattaneo & Michael Jansson & Xinwei Ma, 2019. "Two-Step Estimation and Inference with Possibly Many Included Covariates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1095-1122.
    5. Yukitoshi Matsushita & Taisuke Otsu, 2019. "Jackknife, small bandwidth and high-dimensional asymptotics," STICERD - Econometrics Paper Series 605, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Liu, Lin & Mukherjee, Rajarshi & Robins, James M., 2024. "Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators," Journal of Econometrics, Elsevier, vol. 240(2).
    7. Fernando Rios-Avila, 2019. "A Semi-Parametric Approach to the Oaxaca–Blinder Decomposition with Continuous Group Variable and Self-Selection," Econometrics, MDPI, vol. 7(2), pages 1-29, June.
    8. Amilcar Velez, 2024. "On the Asymptotic Properties of Debiased Machine Learning Estimators," Papers 2411.01864, arXiv.org.
    9. Aurélien Baillon & Owen O'Donnell & Stella Quimbo & Kim van Wilgenburg, 2022. "Do time preferences explain low health insurance take‐up?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 951-983, December.

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