The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
On k-hulls and related problems
SIAM Journal on Computing
Robust regression and outlier detection
Robust regression and outlier detection
k-Violation linear programming
Information Processing Letters
Constructing cuttings in theory and practice
Proceedings of the fourteenth annual symposium on Computational geometry
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
A practical approximation algorithm for the LMS line estimator
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Parametric search made practical
Proceedings of the eighteenth annual symposium on Computational geometry
Short Communication: Least median of squares and regression through the origin
Computational Statistics & Data Analysis
Editorial: Special Issue on Statistical Algorithms and Software
Computational Statistics & Data Analysis
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A common problem in linear regression is that largely aberrant values can strongly influence the results. The least quartile difference (LQD) regression estimator is highly robust, since it can resist up to almost 50% largely deviant data values without becoming extremely biased. Additionally, it shows good behavior on Gaussian data-in contrast to many other robust regression methods. However, the LQD is not widely used yet due to the high computational effort needed when using common algorithms. It is shown that it is possible to compute the LQD estimator for n bivariate data points in expected running time O(n^2logn) or deterministic running time O(n^2log^2n). Additionally, two easy to implement algorithms with slightly inferior time bounds are presented. All of these algorithms are also applicable to least quantile of squares and least median of squares regression through the origin, improving the known time bounds to expected time O(nlogn) and deterministic time O(nlog^2n). The proposed algorithms improve on known results of existing LQD algorithms and hence increase the practical relevance of the LQD estimator.