IDEAS home Printed from https://ideas.repec.org/p/mcm/deptwp/2012-10.html

Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions

Author

Listed:
  • Qi Li
  • Juan Lin
  • Jeffrey S. Racine

Abstract

We propose a data-driven least squares cross-validation method to optimally select smoothing parameters for the nonparametric estimation of conditional cumulative distribution functions and conditional quantile functions. We allow for general multivariate covariates that can be continuous, categorical or a mix of either. We provide asymptotic analysis, examine finite-sample properties via Monte Carlo simulation, and consider an application involving testing for first order stochastic dominance of children's health conditional on parental education and income.

Suggested Citation

  • Qi Li & Juan Lin & Jeffrey S. Racine, 2012. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Department of Economics Working Papers 2012-10, McMaster University.
    • Handle: RePEc:mcm:deptwp:2012-10
    as

    Download full text from publisher

    File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/2012-10.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Esfandiar Maasoumi & Maria Ana Lugo, 2008. "The Information Basis of Multivariate Poverty Assessments," Palgrave Macmillan Books, in: Nanak Kakwani & Jacques Silber (ed.), Quantitative Approaches to Multidimensional Poverty Measurement, chapter 1, pages 1-29, Palgrave Macmillan.
    2. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
    3. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    4. Nicholas Kiefer & Jeffrey Racine, 2009. "The smooth Colonel meets the Reverend," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 521-533.
    5. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
    6. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    7. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    8. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers 17/98, Monash University, Department of Econometrics and Business Statistics.
    9. Chung, Yeonseung & Dunson, David B., 2009. "Nonparametric Bayes Conditional Distribution Modeling With Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1646-1660.
    10. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    11. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(1), pages 169-192, February.
    12. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    13. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    14. Bashtannyk, David M. & Hyndman, Rob J., 2001. "Bandwidth selection for kernel conditional density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 36(3), pages 279-298, May.
    Full references (including those not matched with items on IDEAS)

    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. Lin, Wei & Cai, Zongwu & Li, Zheng & Su, Li, 2015. "Optimal smoothing in nonparametric conditional quantile derivative function estimation," Journal of Econometrics, Elsevier, vol. 188(2), pages 502-513.
    2. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355, December.
    3. Chen, Xirong & Li, Degui & Li, Qi & Li, Zheng, 2019. "Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates," Journal of Econometrics, Elsevier, vol. 212(2), pages 433-450.
    4. Haupt, Harry & Schnurbus, Joachim & Semmler, Willi, 2018. "Estimation of grouped, time-varying convergence in economic growth," Econometrics and Statistics, Elsevier, vol. 8(C), pages 141-158.
    5. repec:wyi:journl:002112 is not listed on IDEAS
    6. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.
    7. Zongwu Cai & Qi Li, 2013. "Some Recent Develop- ments on Nonparametric Econometrics," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    8. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527, arXiv.org, revised Oct 2019.
    9. Li, Dong & Li, Qi, 2010. "Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters," Journal of Econometrics, Elsevier, vol. 157(1), pages 179-190, July.
    10. Nolwenn Roudaut & Anne Vanhems, 2012. "Explaining firms efficiency in the Ivorian manufacturing sector: a robust nonparametric approach," Journal of Productivity Analysis, Springer, vol. 37(2), pages 155-169, April.
    11. Das, Sonali & Racine, Jeffrey S., 2018. "Interactive nonparametric analysis of nonlinear systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 290-301.
    12. Racine, Jeffrey S. & Li, Kevin, 2017. "Nonparametric conditional quantile estimation: A locally weighted quantile kernel approach," Journal of Econometrics, Elsevier, vol. 201(1), pages 72-94.
    13. Arribas Ivan & Perez Francisco & Tortosa-Ausina Emili, 2010. "The Determinants of International Financial Integration Revisited: The Role of Networks and Geographic Neutrality," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(1), pages 1-55, December.
    14. Maasoumi, Esfandiar & Racine, Jeffrey S., 2016. "A solution to aggregation and an application to multidimensional ‘well-being’ frontiers," Journal of Econometrics, Elsevier, vol. 191(2), pages 374-383.
    15. Michael S. Delgado & Daniel J. Henderson & Christopher F. Parmeter, 2014. "Does Education Matter for Economic Growth?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 334-359, June.
    16. Zonglin He & Jean D. Opsomer, 2015. "Local polynomial regression with an ordinal covariate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 516-531, December.
    17. repec:jss:jstsof:27:i05 is not listed on IDEAS
    18. Baležentis, Tomas & De Witte, Kristof, 2015. "One- and multi-directional conditional efficiency measurement – Efficiency in Lithuanian family farms," European Journal of Operational Research, Elsevier, vol. 245(2), pages 612-622.
    19. Norets, Andriy & Pelenis, Justinas, 2012. "Bayesian modeling of joint and conditional distributions," Journal of Econometrics, Elsevier, vol. 168(2), pages 332-346.
    20. Arulampalam, Wiji & Corradi, Valentina & Gutknecht, Daniel, 2024. "Intercept Estimation In Nonlinear Selection Models," Econometric Theory, Cambridge University Press, vol. 40(6), pages 1311-1363, December.
    21. Valentin Zelenyuk & Leopold Simar, 2011. "To Smooth or Not to Smooth? The Case of Discrete Variables in Nonparametric Regressions," CEPA Working Papers Series WP102011, School of Economics, University of Queensland, Australia.

    More about this item

    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:mcm:deptwp:2012-10. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/demcmca.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.