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Confidence Bands In Quantile Regression

  • Härdle, Wolfgang K.
  • Song, Song

Let ( X1 , Y 1), …, ( X, Y ) be independent and identically distributed random variables and let l (x ) be the unknown p -quantile regression curve of Y conditional on X . A quantile smoother l (x ) is a localized, nonlinear estimator of l (x ). The strong uniform consistency rate is established under general conditions. In many applications it is necessary to know the stochastic fluctuation of the process { l( x) – l (x )}. Using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup 0≤ | l( x) − l (x )|. The derived result helps in the construction of a uniform confidence band for the quantile curve l (x ). This confidence band can be applied as a econometric model check. An economic application considers the relation between age and earnings in the labor market by means of parametric model specification tests, which presents a new framework to describe trends in the entire wage distribution in a parsimonious way.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 26 (2010)
Issue (Month): 04 (August)
Pages: 1180-1200

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Handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1180-1200_99
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  1. Murphy, Kevin M & Welch, Finis, 1990. "Empirical Age-Earnings Profiles," Journal of Labor Economics, University of Chicago Press, vol. 8(2), pages 202-29, April.
  2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  3. Haerdle,W. & Janssen,P. & Serfling,R., 1986. "Strong uniform consistency rates for estimators of conditional functionals," Discussion Paper Serie A 63, University of Bonn, Germany.
  4. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
  5. Lejeune, Michel G. & Sarda, Pascal, 1988. "Quantile regression: a nonparametric approach," Computational Statistics & Data Analysis, Elsevier, vol. 6(3), pages 229-239, April.
  6. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010. "Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1529-1564, October.
  7. Kiho Jeong & Wolfgang Härdle, 2008. "A Consistent Nonparametric Test for Causality in Quantile," SFB 649 Discussion Papers SFB649DP2008-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Härdle, Wolfgang, 1989. "Asymptotic maximal deviation of M-smoothers," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 163-179, May.
  9. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
  10. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
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