Small sample corrections for LTS and MCD

By Greet Pison, S. Van Aelst, Gert Willems. 2002

199 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/10a0780a3e549eecb7627d44180b93e1cae32913

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In Statistics and Probability

Citations in the corpus

Outlier detection for high-dimensional data (2015, background): “Like its counterpart in the minimum covariance determinant (Pison et al., 2002), c can be determined as follows.”
Multivariate Outlier Detection With High-Breakdown Estimators (2010, methodology): “(2) The proportionality constant kMCD(h,n, v), depending on the values of h, n, and v, serves the purpose of making ̂(MCD) both consistent and unbiased when each yi ∼ N(μ, ) (Croux and Haesbroeck 1999; Pison, Van Aelst, and Willems 2002).”
Minimum covariance determinant (2010, unknown): “μ̂MCD(AX + b) = Aμ̂MCD(X) + b (7) ̂MCD(AX + b) = ÂMCD(X)A.”
Robust estimation of Cronbach's alpha (2006, methodology): “The factor cn makes the MCD consistent and unbiased at finite-samples (see Pison et al. 2002b).”
A comparison of robust alternatives to Hotelling’s T 2 control chart (2009, methodology): “The MCD location estimator is defined as the sample mean vector of the points in the halfset, and the MCD scale estimator is the sample covariance matrix of the halfset multiplied by a consistency factor [8,20].”
Finding an unknown number of multivariate outliers (2009, methodology): “Pison et al. (2002) showed by Monte Carlo simulation the importance of applying a small sample correction factor to it.”
An Object-Oriented Framework for Robust Multivariate Analysis (2009, unknown): “Again, the multiplication factors c r.ccf and c r.sscf are selected so that C R is consistent at the multivariate normal model and unbiased at small samples (see Pison et al. 2002; Todorov 2008, and the references therein).”
Outlyingness weighted covariation (2011, unknown): “For the hard rejection weight function, cw is 1/Fχ2 N+2 (k) (Croux and Haesbroeck, 1999; Pison et al., 2002).”
Anomaly detection by robust statistics (2017, methodology): “The scale of the errors σ can be estimated by ˆ σ /h where r i are the residuals from the LTS fit, and c h,n is a constant that makes ˆ σ LTS consistent at gaussian error distributions, as described in 27 .”
A Multivariate Robust Control Chart for Individual Observations (2009, methodology): “975, which was advocated and used by Rousseeuw and Van Driessen (1999). Using cη,p = η/P (χ(2)(p+2) ≤ qη) makes SRMCD consistent under the multivariate normal distribution.”