Hennig, CM;
Viroli, C;
(2016)
Quantile-based classifiers.
Biometrika
, 103
(2)
pp. 435-446.
10.1093/biomet/asw015.
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Abstract
Classification with small samples of high-dimensional data is important in many application areas. Quantile classifiers are distance-based classifiers that require a single parameter, regardless of the dimension, and classify observations according to a sum of weighted componentwise distances of the components of an observation to the within-class quantiles. An optimal percentage for the quantiles can be chosen by minimizing the misclassification error in the training sample. It is shown that this choice is consistent for the classification rule with the asymptotically optimal quantile and that under some assumptions, as the number of variables goes to infinity, the probability of correct classification converges to unity. The effect of skewness of the distributions of the predictor variables is discussed. The optimal quantile classifier gives low misclassification rates in a comprehensive simulation study and in a real-data application.
| Type: | Article |
|---|---|
| Title: | Quantile-based classifiers |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/biomet/asw015 |
| Publisher version: | http://dx.doi.org/10.1093/biomet/asw015 |
| Language: | English |
| Additional information: | Copyright © 2016 Biometrika Trust. This is a pre-copyedited, author-produced PDF of an article accepted for publication in Biometrika following peer review. The version of record [Hennig, CM; Viroli, C; (2016) Quantile-based classifiers. Biometrika , 103 (2) pp. 435-446. 10.1093/biomet/asw015] is available online at: http://biomet.oxfordjournals.org/content/103/2/435 |
| Keywords: | High-dimensional data; Median-based classifier; Misclassification rate; Skewness |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1492790 |
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