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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/1986

Title: Quantile regression with monotonicity restrictions using P-splines and the L-1-norm
Authors: BOLLAERTS, Kaatje
Eilers, PHC
Issue Date: 2006
Citation: STATISTICAL MODELLING, 6(3). p. 189-207
Abstract: Quantile regression is an alternative to OLS regression. In quantile regression, the sum of absolute deviations or the L-1-norm is minimized, whereas the sum of squared deviations or the L-2-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-quanti le function to be monotone increasing. In particular, P-splines with an additional asymmetric penalty enforcing monotonicity are used within an L-1-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.
Notes: Univ Hasselt, Ctr Stat, B-3590 Diepenbeek, Belgium.Bollaerts, K, Univ Hasselt, Ctr Stat, Agoralaan 1 Gebouw D, B-3590 Diepenbeek, Belgium.kaatje.bollaerts@uhasselt.be
URI: http://hdl.handle.net/1942/1986
DOI: 10.1191/1471082X06st118oa
ISI #: 000240879500001
ISSN: 1471-082X
Category: A1
Type: Journal Contribution
Validation: ecoom, 2007
Appears in Collections: Research publications

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