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Nonparametric regression M-quantiles

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  • Antoch, J.
  • Janssen, P.

Abstract

For the regression model Yi = m(xi)+[var epsilon]i, i = 1,...,n, robust nonparametric estimators are introduced and studied in Härdle and Gasser (1984). We show that these estimators can be viewed as regression M-quantiles. We then establish a probability inequality and a Bahadur representation for such quantiles and discuss some applications.

Suggested Citation

  • Antoch, J. & Janssen, P., 1989. "Nonparametric regression M-quantiles," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 355-362, September.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:4:p:355-362
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    Cited by:

    1. Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 433-447, February.
    2. Chen, Zehua, 1996. "Conditional Lp-quantiles and their application to the testing of symmetry in non-parametric regression," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 107-115, August.
    3. Bosch, Ronald J. & Ye, Yinyu & Woodworth, George G., 1995. "A convergent algorithm for quantile regression with smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 613-630, June.

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