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Nonparametric Estimation and Inference on Conditional Quantile Processes

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  • Zhongjun Qu

    ()
    (Department of Economics, Boston University)

  • Jungmo Yoon

    ()
    (Robert Day School of Economics and Finance, Claremont Mckenna College)

Abstract

We consider the estimation and inference about a nonparametrically specified con- ditional quantile process. For estimation, a two-step procedure is proposed. The first step utilizes local linear regressions and maintains quantile monotonicity through sim- ple inequality constraints. The second step involves linear interpolation between adja- cent quantiles. When computing the estimator, the bandwidth parameter is allowed to vary across quantiles to adapt to the data sparsity. The procedure is computationally simple to implement and is feasible even for relatively large data sets. For inference, we first obtain a uniform Bahadur-type representation for the conditional quantile process. Then, we show that the estimator converges weakly to a continuous Gaussian process, whose critical values can be estimated via simulations by exploiting the fact that it is conditionally pivotal. Next, we demonstrate how to compute the optimal bandwidth, construct uniform confidence bands and test hypotheses about the quantile process. Finally, we examine the performance of the bandwidth selection rule and the uniform confidence bands through simulations.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2011-059.

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Length: 62 pages
Date of creation: Jan 2011
Date of revision:
Handle: RePEc:bos:wpaper:wp2011-059

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Related research

Keywords: nonparametric quantile regression; monotonicity constraint; uniform Bahadur representation; uniform inference;

References

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  1. Härdle, Wolfgang K. & Song, Song, 2010. "Confidence Bands In Quantile Regression," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1180-1200, August.
  2. Holger Dette & Stanislav Volgushev, 2008. "Non-crossing non-parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627.
  3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, April.
  4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  5. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, 01.
  6. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves without Crossing," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
  7. Zhongjun Qu & Tatsushi Oka, 2010. "Estimating structural changes in regression quantiles," Boston University - Department of Economics - Working Papers Series WP2010-052, Boston University - Department of Economics.
  8. Bai, Jushan, 1996. "Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach," Econometrica, Econometric Society, vol. 64(3), pages 597-622, May.
  9. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
  10. Neocleous, Tereza & Portnoy, Stephen, 2008. "On monotonicity of regression quantile functions," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1226-1229, August.
  11. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
  12. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Finite sample inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 152(2), pages 93-103, October.
  13. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  14. Heckman, James J & Smith, Jeffrey, 1997. "Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 487-535, October.
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