Computing LTS Regression for Large Data Sets

By Peter J. Rousseeuw, Katrien van Driessen. 2005

619 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Robust Regression via Hard Thresholding (2015, neutral): “1805.”
Learning with Bad Training Data via Iterative Trimmed Loss Minimization (2018, neutral): “For example, see [H¨os95, RVD06, SSvdHT13] for algorithm solutions ﬁnding the least trimmed loss estimator in linear regression setting.”
Anomaly detection by robust statistics (2017, methodology): “A fast algorithm for the LTS estimator (FAST-LTS) has been developed 26 .”
Robust linear regression for high‐dimensional data: An overview (2020, methodology): “It has been shown (Rousseeuw & Van Driessen, 2006) that the objective function of LTS decreases successively: X i∈H2 ri β̂H2 2 ≤ X i∈H1 ri β̂H1 2 Thus, Steps 2 and 3 are alternated until convergence.”
Robust statistics for outlier detection (2011, background): “22 The scale of the errors σ can be estimated by ˆ σ 2LTS = c 2 h , n (cid:2) = 1 ( r 2 ) ( i ) / h , where r i are the residuals from the LTS ﬁt and c h , n is a constant that makes ˆ σ unbiased at Gaussian error distributions.”
Heuristic Optimization Methods in Econometrics (2009, methodology): “To illustrate the computation of an LMS estimator we use a data generation process which has been borrowed from Salibian-Barrera and Yohai (2004). We consider model (6) where 90% of the observed variables are i.”
Background removal from spectra by designing and minimising a non-quadratic cost function (2005, neutral): “The proposed methods are then linked with available approaches such as least trimmed squares [18] and the method proposed in [3] for which a mathematical foundation is provided.”
Is tolerance good or bad for growth? (2010, neutral): “23 For more on the LTS estimator and its application, see Verboven and Hubert (2005) and Rousseeuw and Van Driessen (2006) .”
An Object-Oriented Framework for Robust Multivariate Analysis (2009, neutral): “Fast S estimates : Salibian-Barrera and Yohai (2006) proposed a fast algorithm for regression S estimates similar to the FAST-LTS algorithm of Rousseeuw and Van Driessen (2006) and borrowing ideas from the SURREAL algorithm of Ruppert (1992).”
Breakdown Point and Computation of Trimmed Likelihood Estimators in Generalized Linear Models (2003, methodology): “However, following the same reasoning as Rousseeuw and Van Driessen [26] and because θ̂old can be arbitrary, one should draw subsamples with a smaller k∗ := N (X) + 1 size as the chance to get at least one outlier free subsample is larger.”
RAVE—A Detector-Independent Toolkit to Reconstruct Vertices (2011, methodology): “For non-Gaussian parameters, the Gaussian-sum technique was considered [14], protection against outlying or mis-measured tracks was introduced with robust techniques such as the M-estimator [15] or trimming techniques [16], [17]; later the adaptive technique was established [16], [18], [19].”
The ATLAS3D project – XX. Mass–size and mass–σ distributions of early-type galaxies: bulge fraction drives kinematics, mass-to-light ratio, molecular gas fraction and stellar initial mass function (2012, methodology): “…parameter (M/L)stars/(M/L)Salp and the logarithm of σ e, using the robust linear fitting routine LTS_LINEFIT presented5 in Paper XV, which combines the Least Trimmed Squares robust technique of Rousseeuw & Driessen (2006) into a least-squares fitting algorithm which allows for intrinsic scatter.”