Regression Quantiles(分位数开山之作，Koenker, R. and G. Bassett ,Econometrica1978)
Regression Quantiles
Author(s): Roger Koenker and Gilbert Bassett, Jr.
Reviewed work(s):
Source: Econometrica, Vol. 46, No. 1 (Jan., 1978), pp. 33-50
Published by: The Econometric Society
Stable URL: http://www.jstor.org/stable/1913643 .
Accessed: 13/03/2012 ...
Regression Quantiles
Author(s): Roger Koenker and Gilbert Bassett, Jr.
Reviewed work(s):
Source: Econometrica, Vol. 46, No. 1 (Jan., 1978), pp. 33-50
Published by: The Econometric Society
Stable URL: http://www.jstor.org/stable/1913643 .
Accessed: 13/03/2012 13:03
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Econometrica, Vol. 46, No. 1 (January, 1978)
REGRESSION QUANTILES'
BY ROGER KOENKER AND GILBERT BASSETT, JR.
A simple minimization problem yielding the ordinary sample quantiles in the location
model is shown to generalize naturally to the linear model generating a new class of
statistics we term "regression quantiles." The estimator which minimizes the sum of
absolute residuals is an important special case. Some equivariance properties and the joint
asymptotic distribution of regression quantiles are established. These results permit a
natural generalization to the linear model of certain well-known robust estimators of
location.
Estimators are suggested, which have comparable efficiency to least squares for
Gaussian linear models while substantially out-performing the least-squares estimator
over a wide class of non-Gaussian error distributions.
1. INTRODUCTION
IN STATISTICAL PARLANCE the term robustness has come to connote a certain
resilience of statistical procedures to deviations from the assumptions of
hypothetical models. The paradigm may be briefly stated as follows.2 The process
generating observed data is thought to be approximately described by an element
of some parametric class of models. The investigator seeks statistics, i.e., a
mapping from the sample space to a parameter space, whose distribution will be as
concentrated as possible near the true parameters-if the hypothesized model is
correct. If however, as seems almost certain, the parametric model is not quite
true, one would like to use estimators whose distributions were altered only
slightly if the distribution of the observations were close, in some reasonable
sense, to that of some member of the parametric class. In important special cases
this modest robustness requirement is not met by estimators in common use.3
We consider the familiar problem of estimating a vector of unknown (regres-
sion) parameters, 1B, from a sample of independent observations on random
variables Y,, Y2,. . ., YT, distributed according to
(1. 1) P(Yt
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