Confidence Intervals for Regression Quantiles

  • Roger Koenker
Conference paper

DOI: 10.1007/978-3-642-57984-4_29

Part of the book series Contributions to Statistics (CONTRIB.STAT.)
Cite this paper as:
Koenker R. (1994) Confidence Intervals for Regression Quantiles. In: Mandl P., Hušková M. (eds) Asymptotic Statistics. Contributions to Statistics. Physica, Heidelberg


Several methods to construct confidence intervals for regression quan-tile estimators (Koenker and Bassett (1978)) are reviewed. Direct estimation of the asymptotic covariance matrix requires an estimate of the reciprocal of the error density (sparsity function) at the quantite of interest; some recent work on bandwidth selection for this problem will be discussed. Several versions of the bootstrap for quantile regression will be described as well as a recent proposal by Parzen, Wei, and Ying (1992) for resampling from the (approximately pivotal) estimating equation. Finally, we will describe a new approach based on inversion of a rank test suggested by Gutenbrunner, Jurečková, Koenker, and Portnoy (1993) and introduced in Hušková(1994). The latter approach has several advantages: it may be computed relatively efficiently, it is consistent under certain heteroskedastic conditions and it circumvents any explicit estimation of the sparsity function. A small monte-carlo experiment is employed to compare the competing methods.

AMS 1980 Subject Classification

62G10 62J10 


regression quantiles confidence intervals rank tests bootstrapping sparsity estimation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Roger Koenker
    • 1
  1. 1.University of IllinoisChampaign-UrbanaUSA