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An adaptive algorithm for quantile regression. (English) Zbl 1088.62092

Hubert, Mia (ed.) et al., Theory and applications of recent robust methods. Selected papers of the international conference on robust statistics 2003, ICORS 2003, Antwerp, Belgium, July 13–18, 2003. Basel: Birkhäuser (ISBN 3-7643-7060-2/hbk). Statistics for Industry and Technology, 39-48 (2004).
Summary: We introduce an algorithm to compute regression quantile functions. This algorithm combines three algorithms – the simplex, interior point, and smoothing algorithm. The simplex and interior point algorithms come from the background of linear programming. While the simplex method can handle small to middle sized data sets, the interior point method can handle large to huge data sets efficiently. The smoothing algorithm is specially designed for the \(L_1\) or quantile regression type of problems, and it outperforms the other two algorithms for fat data sets. Combining these three algorithms produces an algorithm, which is adaptive in the sense that it can intelligently detect the input data sets and select one of the three algorithms to efficiently compute the regression quantile functions.
For the entire collection see [Zbl 1047.62002].

MSC:

62J99 Linear inference, regression
62F35 Robustness and adaptive procedures (parametric inference)
90C90 Applications of mathematical programming
65C60 Computational problems in statistics (MSC2010)
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