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Uniform Bias Study and Bahadur Representation for Local Polynomial Estimators of the Conditional Quantile Function

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  • Emmanuel Guerre

    ()
    (Queen Mary, University of London)

  • Camille Sabbah

    ()
    (Universit� Pierre et Marie Curie, Paris)

Abstract

This paper investigates the bias and the 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 that 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 to obtain a simple estimator of the conditional quantile function of the private values in a first price sealed bids auctions under the independent private values paradigm and risk neutrality.

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Bibliographic Info

Paper provided by Queen Mary, University of London, School of Economics and Finance in its series Working Papers with number 648.

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Date of creation: Sep 2009
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Handle: RePEc:qmw:qmwecw:wp648

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Keywords: Bahadur representation; Conditional quantile function; Local polynomial estimation; Econometrics of auctions;

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References

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  1. 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, 07.
  2. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  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.
  5. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
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Cited by:
  1. Efang Kong & Oliver Linton & Yingcun Xia, 2011. "Global Bahadur representation for nonparametric censored regression quantiles and its applications," CeMMAP working papers CWP33/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Härdle, 2014. "Confidence Corridors for Multivariate Generalized Quantile Regression," SFB 649 Discussion Papers SFB649DP2014-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Sokbae 'Simon' Lee & Kyungchul Song & Yoon-Jae Whang, 2014. "Testing for a general class of functional inequalities," CeMMAP working papers CWP09/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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