A practical approximation algorithm for the LTS estimator

The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear model to a set of points. It was proposed by Rousseeuw as a robust alternative to the classical least squares estimator. Given a set of n points in Rd, the objective is to minimize the sum of the smalles...

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Vydáno v:Computational statistics & data analysis Ročník 99; s. 148 - 170
Hlavní autoři: Mount, David M., Netanyahu, Nathan S., Piatko, Christine D., Wu, Angela Y., Silverman, Ruth
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.07.2016
Témata:
Accuracy
Algorithms
Approximation
Approximation algorithms
Computation
Computational geometry
data collection
Estimators
Least trimmed squares
Linear estimation
linear models
Mathematical analysis
Mathematical models
probability analysis
Robust estimation
Slopes
Least trimmed squares
Computational geometry
Approximation algorithms
Robust estimation
Linear estimation
ISSN:0167-9473, 1872-7352
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Shrnutí:The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear model to a set of points. It was proposed by Rousseeuw as a robust alternative to the classical least squares estimator. Given a set of n points in Rd, the objective is to minimize the sum of the smallest 50% squared residuals (or more generally any given fraction). There exist practical heuristics for computing the linear LTS estimator, but they provide no guarantees on the accuracy of the final result. Two results are presented. First, a measure of the numerical condition of a set of points is introduced. Based on this measure, a probabilistic analysis of the accuracy of the best LTS fit resulting from a set of random elemental fits is presented. This analysis shows that as the condition of the point set improves, the accuracy of the resulting fit also increases. Second, a new approximation algorithm for LTS, called Adaptive-LTS, is described. Given bounds on the minimum and maximum slope coefficients, this algorithm returns an approximation to the optimal LTS fit whose slope coefficients lie within the given bounds. Empirical evidence of this algorithm’s efficiency and effectiveness is provided for a variety of data sets.
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ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2016.01.016