IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v28y2012i01p87-129_00.html
   My bibliography  Save this article

Uniform Bias Study And Bahadur Representation For Local Polynomial Estimators Of The Conditional Quantile Function

Author

Listed:
  • Guerre, Emmanuel
  • Sabbah, Camille

Abstract

This paper investigates the bias and the weak Bahadur representation of a local polynomial estimator of the conditional quantile function and its derivatives. The bias and Bahadur remainder term are studied uniformly with respect to the quantile level, the covariates, and the smoothing parameter. The order of the local polynomial estimator can be higher than the differentiability order of the conditional quantile function. Applications of the results deal with global optimal consistency rates of the local polynomial quantile estimator, performance of random bandwidths, and estimation of the conditional quantile density function. The latter allows us to obtain a simple estimator of the conditional quantile function of the private values in a first-price sealed bids auction under the independent private values paradigm and risk neutrality.

Suggested Citation

  • Guerre, Emmanuel & Sabbah, Camille, 2012. "Uniform Bias Study And Bahadur Representation For Local Polynomial Estimators Of The Conditional Quantile Function," Econometric Theory, Cambridge University Press, vol. 28(01), pages 87-129, February.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:01:p:87-129_00
    as

    Download full text from publisher

    File URL: http://journals.cambridge.org/abstract_S0266466611000132
    File Function: link to article abstract page
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
    2. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2009. "Nonparametric Identification of Risk Aversion in First-Price Auctions Under Exclusion Restrictions," Econometrica, Econometric Society, vol. 77(4), pages 1193-1227, July.
    3. 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.
    4. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, vol. 167(2), pages 345-357.
    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. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Karl Härdle, 2017. "Confidence Corridors for Multivariate Generalized Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 70-85, January.
    2. David M. Kaplan & Matt Goldman, 2011. "Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics," Working Papers 1503, Department of Economics, University of Missouri, revised 21 Nov 2016.
    3. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val, 2011. "Conditional quantile processes based on series or many regressors," CeMMAP working papers CWP19/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Kaplan, David M., 2015. "Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion," Journal of Econometrics, Elsevier, vol. 185(1), pages 20-32.
    5. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2013. "Global Bahadur Representation For Nonparametric Censored Regression Quantiles And Its Applications," Econometric Theory, Cambridge University Press, vol. 29(05), pages 941-968, October.
    6. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    7. Joel L. Horowitz & Anand Krishnamurthy, 2017. "A bootstrap method for constructing pointwise and uniform confidence bands for conditional quantile functions," CeMMAP working papers CWP01/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Nathalie Gimenes, 2014. "Econometrics of Ascending Auctions by Quantile Regression," Working Papers, Department of Economics 2014_25, University of São Paulo (FEA-USP).
    9. Sokbae Lee & Kyungchul Song & Yoon-Jae Whang, 2014. "Testing For A General Class Of Functional Inequalities," KIER Working Papers 889, Kyoto University, Institute of Economic Research.
    10. Christou, Eliana & Akritas, Michael G., 2016. "Single index quantile regression for heteroscedastic data," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 169-182.
    11. Fan, Yanqin & Guerre, Emmanuel & Zhu, Dongming, 2017. "Partial identification of functionals of the joint distribution of “potential outcomes”," Journal of Econometrics, Elsevier, vol. 197(1), pages 42-59.
    12. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    13. Fernandes, Marcelo & Guerre, Emmanuel & Horta, Eduardo, 2017. "Smoothing quantile regressions," Textos para discussão 457, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    14. David M. Kaplan, 2013. "IDEAL Inference on Conditional Quantiles via Interpolated Duals of Exact Analytic L-statistics," Working Papers 1316, Department of Economics, University of Missouri.
    15. Zhao, Weihua & Lian, Heng, 2017. "Quantile index coefficient model with variable selection," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 40-58.
    16. Nathalie Gimenes & Emmanuel Guerre, 2016. "Quantile methods for first-price auction: A signal approach," Working Papers, Department of Economics 2016_23, University of São Paulo (FEA-USP).

    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

    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:cup:etheor:v:28:y:2012:i:01:p:87-129_00. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters). General contact details of provider: http://journals.cambridge.org/jid_ECT .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.