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https://hdl.handle.net/20.500.14279/1976
Τίτλος: | An exact least trimmed squares algorithm for a range of coverage values | Συγγραφείς: | Hofmann, Marc H. Gatu, Cristian Kontoghiorghes, Erricos John |
Major Field of Science: | Social Sciences | Field Category: | SOCIAL SCIENCES | Λέξεις-κλειδιά: | Outliers;QR factorization;Regression tree algorithms;Robust estimation | Ημερομηνία Έκδοσης: | 2010 | Πηγή: | Journal of Computational and Graphical Statistics, 2010, vol. 19, no. 1, pp. 191-204 | Volume: | 19 | Issue: | 1 | Start page: | 191 | End page: | 204 | Περιοδικό: | Journal of Computational and Graphical Statistics | Περίληψη: | A new algorithm to solve exact least trimmed squares (LTS) regression is presented. The adding row algorithm (ARA) extends existing methods that compute the LTS estimator for a given coverage. It employs a tree-based strategy to compute a set of LTS regressors for a range of coverage values. Thus, prior knowledge of the optimal coverage is not required. New nodes in the regression tree are generated by updating the QR decomposition of the data matrix after adding one observation to the regression model. The ARA is enhanced by employing a branch and bound strategy. The branch and bound algorithm is an exhaustive algorithm that uses a cutting test to prune nonoptimal subtrees. It significantly improves over the ARA in computational performance. Observation preordering throughout the traversal of the regression tree is investigated. A computationally efficient and numerically stable calculation of the bounds using Givens rotations is designed around the QR decomposition, avoiding the need to explicitly update the triangular factor when an observation is added. This reduces the overall computational load of the preordering device by approximately half. A solution is proposed to allow preordering when the model is underdetermined. It employs pseudo-orthogonal rotations to downdate the QR decomposition. The strategies are illustrated by example. Experimental results confirm the computational efficiency of the proposed algorithms. Supplemental materials (R package and formal proofs) are available online | URI: | https://hdl.handle.net/20.500.14279/1976 | ISSN: | 15372715 | DOI: | 10.1198/jcgs.2009.07091 | Rights: | © American Statistical Association | Type: | Article | Affiliation: | Cyprus University of Technology | Affiliation: | Université de Neuchâtel Alexandru Ioan Cuza University of Iaşi University of Cyprus University of London Cyprus University of Technology |
Publication Type: | Peer Reviewed |
Εμφανίζεται στις συλλογές: | Άρθρα/Articles |
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