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Generalized Jackknife Estimators of Weighted Average Derivatives

Author

Listed:
  • Matias D. Cattaneo
  • Richard K. Crump
  • Michael Jansson

Abstract

With the aim of improving the quality of asymptotic distributional approximations for nonlinear functionals of nonparametric estimators, this article revisits the large-sample properties of an important member of that class, namely a kernel-based weighted average derivative estimator. Asymptotic linearity of the estimator is established under weak conditions. Indeed, we show that the bandwidth conditions employed are necessary in some cases. A bias-corrected version of the estimator is proposed and shown to be asymptotically linear under yet weaker bandwidth conditions. Implementational details of the estimators are discussed, including bandwidth selection procedures. Consistency of an analog estimator of the asymptotic variance is also established. Numerical results from a simulation study and an empirical illustration are reported. To establish the results, a novel result on uniform convergence rates for kernel estimators is obtained. The online supplemental material to this article includes details on the theoretical proofs and other analytic derivations, and further results from the simulation study.

Suggested Citation

  • Matias D. Cattaneo & Richard K. Crump & Michael Jansson, 2013. "Generalized Jackknife Estimators of Weighted Average Derivatives," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1243-1256, December.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:504:p:1243-1256
    DOI: 10.1080/01621459.2012.745810
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    Cited by:

    1. Matias D. Cattaneo & Max H. Farrell & Michael Jansson & Ricardo Masini, 2022. "Higher-order Refinements of Small Bandwidth Asymptotics for Density-Weighted Average Derivative Estimators," Papers 2301.00277, arXiv.org, revised Feb 2024.
    2. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    3. Ang, Andrew & Kristensen, Dennis, 2012. "Testing conditional factor models," Journal of Financial Economics, Elsevier, vol. 106(1), pages 132-156.
    4. 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.
    5. Rothe, Christoph & Firpo, Sergio Pinheiro, 2013. "Semiparametric estimation and inference using doubly robust moment conditions," Textos para discussão 330, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    6. Matias D. Cattaneo & Michael Jansson, 2014. "Bootstrapping Kernel-Based Semiparametric Estimators," CREATES Research Papers 2014-25, Department of Economics and Business Economics, Aarhus University.
    7. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    8. Cattaneo, Matias D. & Jansson, Michael, 2022. "Average Density Estimators: Efficiency And Bootstrap Consistency," Econometric Theory, Cambridge University Press, vol. 38(6), pages 1140-1174, December.
    9. Yukitoshi Matsushita & Taisuke Otsu, 2018. "Likelihood Inference on Semiparametric Models: Average Derivative and Treatment Effect," The Japanese Economic Review, Japanese Economic Association, vol. 69(2), pages 133-155, June.
    10. Cizek, Pavel & Sadikoglu, Serhan, 2022. "Nonseparable Panel Models with Index Structure and Correlated Random Effects," Other publications TiSEM 7899deb9-0eda-47e6-a3b8-2, Tilburg University, School of Economics and Management.
    11. Max H. Farrell, 2013. "Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations," Papers 1309.4686, arXiv.org, revised Feb 2018.
    12. 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.
    13. Harold D. Chiang & Bing Yang Tan, 2020. "Empirical likelihood and uniform convergence rates for dyadic kernel density estimation," Papers 2010.08838, arXiv.org, revised May 2022.
    14. Čížek, Pavel & Lei, Jinghua, 2018. "Identification and estimation of nonseparable single-index models in panel data with correlated random effects," Journal of Econometrics, Elsevier, vol. 203(1), pages 113-128.
    15. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    16. 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.
    17. Jia Li & Dacheng Xiu, 2016. "Generalized Method of Integrated Moments for High‐Frequency Data," Econometrica, Econometric Society, vol. 84(4), pages 1613-1633, July.
    18. Nagasawa, Kenichi, 2020. "Identification and Estimation of Group-Level Partial Effects," The Warwick Economics Research Paper Series (TWERPS) 1243, University of Warwick, Department of Economics.
    19. Ruijun Bu & Jihyun Kim & Bin Wang, 2020. "Uniform and Lp Convergences of Nonparametric Estimation for Diffusion Models," Working Papers 202021, University of Liverpool, Department of Economics.
    20. 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.
    21. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    22. Max H. Farrell & Tengyuan Liang & Sanjog Misra, 2020. "Deep Learning for Individual Heterogeneity: An Automatic Inference Framework," Papers 2010.14694, arXiv.org, revised Jul 2021.

    More about this item

    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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