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On monotonicity of regression quantile functions

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  • Neocleous, Tereza
  • Portnoy, Stephen
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 78 (2008)
    Issue (Month): 10 (August)
    Pages: 1226-1229

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    Handle: RePEc:eee:stapro:v:78:y:2008:i:10:p:1226-1229

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    References

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    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. 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.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
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    Cited by:
    1. Zhongjun Qu & Jungmo Yoon, 2011. "Nonparametric Estimation and Inference on Conditional Quantile Processes," Boston University - Department of Economics - Working Papers Series WP2011-059, Boston University - Department of Economics.
    2. 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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