Statistical Modelling 6 (2006), 189–207
Quantile regression with monotonicity restrictions using
P-splines and the L1-norm
Kaatje Bollaerts
University Hasselt,
Center for Statistics,
Agoralaan 1 Gebouw D,
B–3590 Diepenbeek
Belgium
eMail:
kaatje.bollaerts@uhasselt.be
Paul H.C. Eilers
Leids University Medical Center
Belgium
Marc Aerts
Center for Statistics, University Hasselt
Belgium
Abstract:
Quantile regression is an alternative to OLS regression. In quantile
regression, the sum of absolute deviations or the
L1-norm is minimized, whereas the sum of squared
deviations or the L2-norm is minimized in OLS
regression. Quantile regression has the advantage over OLS-regression
of being more robust to outlying observations. Furthermore, quantile
regression provides information complementing the information
provided by OLS-regression. In this study, a non-parametric
approach to quantile regression is presented, which constrains
the estimated-quantile function to be monotone increasing. In
particular, P-splines with an additional asymmetric
penalty enforcing monotonicity are used within an
L1-framework. This can be translated into
a linear programming problem, which will be solved using an
interior point algorithm. As an illustration, the presented
approach will be applied to estimate quantile growth curves
and quantile antibody levels as a function of age.
Keywords:
growth curves; interior point; L1-norm;
monotonicity; P-splines; quantile regression
Downloads:
Software and
example data in zipped archive
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