Ktisis Cyprus University of Technologyhttps://ktisis.cut.ac.cyThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 17 Nov 2019 22:20:06 GMT2019-11-17T22:20:06Z5031An exact least trimmed squares algorithm for a range of coverage valueshttps://ktisis.cut.ac.cy/handle/10488/6712Title: An exact least trimmed squares algorithm for a range of coverage values
Authors: Hofmann, Marc H.; Gatu, Cristian; Kontoghiorghes, Erricos John
Abstract: 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
Fri, 01 Jan 2010 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/67122010-01-01T00:00:00ZEfficient algorithms for computing the best subset regression models for large-scale problemshttps://ktisis.cut.ac.cy/handle/10488/6744Title: Efficient algorithms for computing the best subset regression models for large-scale problems
Authors: Hofmann, Marc H.; Gatu, Cristian; Kontoghiorghes, Erricos John
Abstract: Several strategies for computing the best subset regression models are proposed. Some of the algorithms are modified versions of existing regression-tree methods, while others are new. The first algorithm selects the best subset models within a given size range. It uses a reduced search space and is found to outperform computationally the existing branch-and-bound algorithm. The properties and computational aspects of the proposed algorithm are discussed in detail. The second new algorithm preorders the variables inside the regression tree. A radius is defined in order to measure the distance of a node from the root of the tree. The algorithm applies the preordering to all nodes which have a smaller distance than a certain radius that is given a priori. An efficient method of preordering the variables is employed. The experimental results indicate that the algorithm performs best when preordering is employed on a radius of between one quarter and one third of the number of variables. The algorithm has been applied with such a radius to tackle large-scale subset-selection problems that are considered to be computationally infeasible by conventional exhaustive-selection methods. A class of new heuristic strategies is also proposed. The most important of these is one that assigns a different tolerance value to each subset model size. This strategy with different kind of tolerances is equivalent to all exhaustive and heuristic subset-selection strategies. In addition the strategy can be used to investigate submodels having noncontiguous size ranges. Its implementation provides a flexible tool for tackling large scale models.
Mon, 01 Jan 2007 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/67442007-01-01T00:00:00ZMatrix strategies for computing the least trimmed squares estimation of the general linear and sur modelshttps://ktisis.cut.ac.cy/handle/10488/6723Title: Matrix strategies for computing the least trimmed squares estimation of the general linear and sur models
Authors: Hofmann, Marc H.; Kontoghiorghes, Erricos John
Abstract: An algorithm for computing the exact least trimmed squares (LTS) estimator of the standard regression model has recently been proposed. The LTS algorithm is adapted to the general linear and seemingly unrelated regressions models with possible singular dispersion matrices. It searches through a regression tree to find the optimal estimates and has combinatorial complexity. The model is formulated as a generalized linear least squares problem. Efficient matrix techniques are employed to update the generalized residual sum of squares of a subset model. Specifically, the new algorithm utilizes previous computations to update a generalized QR decomposition by a single row. The sparse structure of the model is exploited. Theoretical measures of computational complexity are provided. Experimental results confirm the ability of the new algorithms to identify outlying observations.
Fri, 01 Jan 2010 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/67232010-01-01T00:00:00Z