IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/113436.html

Rates of expansions for functional estimators

Author

Listed:
  • Kotlyarova, Yulia
  • Schafgans, Marcia M.A.
  • Zinde-Walsh, Victoria

Abstract

In this paper, we summarize results on convergence rates of various kernel based non- and semiparametric estimators, focusing on the impact of insufficient distributional smoothness, possibly unknown smoothness and even non-existence of density. In the presence of a possible lack of smoothness and the uncertainty about smoothness, methods of safeguarding against this uncertainty are surveyed with emphasis on nonconvex model averaging. This approach can be implemented via a combined estimator that selects weights based on minimizing the asymptotic mean squared error. In order to evaluate the finite sample performance of these and similar estimators we argue that it is important to account for possible lack of smoothness.

Suggested Citation

  • Kotlyarova, Yulia & Schafgans, Marcia M.A. & Zinde-Walsh, Victoria, 2021. "Rates of expansions for functional estimators," LSE Research Online Documents on Economics 113436, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:113436
    as

    Download full text from publisher

    File URL: https://researchonline.lse.ac.uk/id/eprint/113436/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Zinde-Walsh, Victoria, 2017. "Kernel Estimation When Density May Not Exist: A Corrigendum," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1259-1263, October.
    3. Zhang, Xinyu & Liu, Chu-An, 2019. "Inference After Model Averaging In Linear Regression Models," Econometric Theory, Cambridge University Press, vol. 35(4), pages 816-841, August.
    4. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    5. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2014. "Bootstrapping Density-Weighted Average Derivatives," Econometric Theory, Cambridge University Press, vol. 30(6), pages 1135-1164, December.
    6. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, January.
    7. Li, Degui & Linton, Oliver & Lu, Zudi, 2015. "A flexible semiparametric forecasting model for time series," Journal of Econometrics, Elsevier, vol. 187(1), pages 345-357.
    8. 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.
    9. Yulia Kotlyarova & Marcia Schafgans & Victoria Zinde-Walsh, 2011. "Adapting Kernel Estimation to Uncertain Smoothness," Working Papers daleconwp2011-01, Dalhousie University, Department of Economics.
    10. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, May.
    11. Lalley, Steven P. & Nobel, Andrew, 2003. "Indistinguishability of absolutely continuous and singular distributions," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 145-154, April.
    12. Kotlyarova, Yulia & Zinde-Walsh, Victoria, 2006. "Non- and semi-parametric estimation in models with unknown smoothness," Economics Letters, Elsevier, vol. 93(3), pages 379-386, December.
    13. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    14. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    15. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413, January.
    16. Aman Ullah & Huansha Wang, 2013. "Parametric and Nonparametric Frequentist Model Selection and Model Averaging," Econometrics, MDPI, vol. 1(2), pages 1-23, September.
    17. Srinivasan, T N, 1970. "Approximations to Finite Sample Moments of Estimators Whose Exact Sampling Distributions are Unknown," Econometrica, Econometric Society, vol. 38(3), pages 533-541, May.
    18. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
    19. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    20. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December.
    21. Purevdorj Tuvaandorj & Victoria Zinde-Walsh, 2014. "Limit Theory and Inference About Conditional Distributions," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 33, pages 397-423, Emerald Group Publishing Limited.
    22. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    23. Marcia M. A. Schafgans & Victoria Zinde-Walsh, 2010. "Smoothness adaptive average derivative estimation," Econometrics Journal, Royal Economic Society, vol. 13(1), pages 40-62, February.
    24. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    25. repec:cep:stiecm:/2011/557 is not listed on IDEAS
    26. 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.
    27. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2014. "Small Bandwidth Asymptotics For Density-Weighted Average Derivatives," Econometric Theory, Cambridge University Press, vol. 30(1), pages 176-200, February.
    28. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    29. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    30. Chen, Xiaohong & Linton, Oliver & Robinson, Peter, 2001. "The estimation of conditional densities," LSE Research Online Documents on Economics 2312, London School of Economics and Political Science, LSE Library.
    31. Liu, Chu-An, 2018. "Averaging estimators for kernel regressions," Economics Letters, Elsevier, vol. 171(C), pages 102-105.
    32. Jeff Racine & Qi Li & Xi Zhu, 2004. "Kernel Estimation of Multivariate Conditional Distributions," Annals of Economics and Finance, Society for AEF, vol. 5(2), pages 211-235, November.
    33. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    34. Yulia Kotlyarova & Marcia M. A. Schafgans & Victoria Zinde-Walsh, 2016. "Smoothness: Bias and Efficiency of Nonparametric Kernel Estimators," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 561-589, Emerald Group Publishing Limited.
    35. Whitney Newey & Fushing Hsieh & James Robins, 1998. "Undersmoothing and Bias Corrected Functional Estimation," Working papers 98-17, Massachusetts Institute of Technology (MIT), Department of Economics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. is not listed on IDEAS
    2. Yong Bao & Aman Ullah, 2021. "The Special Issue in Honor of Anirudh Lal Nagar: An Introduction," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 1-8, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355, December.
    2. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    3. repec:cep:stiecm:/2011/557 is not listed on IDEAS
    4. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    5. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    6. Kotlyarova, Yulia & Schafgans, Marcia M. A. & Zinde‐Walsh, Victoria, 2011. "Adapting kernel estimation to uncertain smoothness," LSE Research Online Documents on Economics 42015, London School of Economics and Political Science, LSE Library.
    7. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, Department of Economics and Business Economics, Aarhus University.
    8. 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.
    9. 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).
    10. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    11. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Nov 2024.
    12. 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).
    13. Shi, Ruoyao, 2024. "An Averaging Estimator For Two-Step M-Estimation In Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 40(3), pages 652-687, June.
    14. Hidehiko Ichimura & Oliver Linton, 2001. "Asymptotic expansions for some semiparametric program evaluation estimators," CeMMAP working papers 04/01, Institute for Fiscal Studies.
    15. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    16. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    17. Ang, Andrew & Kristensen, Dennis, 2012. "Testing conditional factor models," Journal of Financial Economics, Elsevier, vol. 106(1), pages 132-156.
    18. Agboola, Oluwagbenga David & Yu, Han, 2023. "Neighborhood-based cross fitting approach to treatment effects with high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 186(C).
    19. Matias D. Cattaneo & Michael Jansson, 2014. "Bootstrapping Kernel-Based Semiparametric Estimators," CREATES Research Papers 2014-25, Department of Economics and Business Economics, Aarhus University.
    20. Wan, Yuanyuan & Xu, Haiqing, 2015. "Inference in semiparametric binary response models with interval data," Journal of Econometrics, Elsevier, vol. 184(2), pages 347-360.
    21. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • N0 - Economic History - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ehl:lserod:113436. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.