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On monotonicity of regression quantile functions

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  • Neocleous, Tereza
  • Portnoy, Stephen

Abstract

In the linear regression quantile model, the conditional quantile of the response, Y, given x is QYx([tau])[reverse not equivalent]x'[beta]([tau]). Though QYx([tau]) must be monotonically increasing, the Koenker-Bassett regression quantile estimator, , is not monotonic outside a vanishingly small neighborhood of . Given a grid of mesh [delta]n, let be the linear interpolation of the values of along the grid. We show here that for a range of rates, [delta]n, will be strictly monotonic (with probability tending to one) and will be asymptotically equivalent to in the sense that n1/2 times the difference tends to zero at a rate depending on [delta]n.

Suggested Citation

  • Neocleous, Tereza & Portnoy, Stephen, 2008. "On monotonicity of regression quantile functions," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1226-1229, August.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:10:p:1226-1229
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    References listed on IDEAS

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    1. Portnoy, Stephen, 1991. "Asymptotic behavior of regression quantiles in non-stationary, dependent cases," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 100-113, July.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, April.
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    Cited by:

    1. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    2. Juban, Romain & Ohlsson, Henrik & Maasoumy, Mehdi & Poirier, Louis & Kolter, J. Zico, 2016. "A multiple quantile regression approach to the wind, solar, and price tracks of GEFCom2014," International Journal of Forecasting, Elsevier, vol. 32(3), pages 1094-1102.
    3. Peng, Limin, 2012. "Self-consistent estimation of censored quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 368-379.

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