MATLAB library LIBRA

LIBRA stands for ‘library for robust analysis.’ It is a MATLAB toolbox mainly containing implementations of robust statistical methods. Robust statistics is involved with the detection of aberrant observations, also called outliers. The aim of robust statistical methods is to provide estimates which are not affected by the nonregular observations and which are then able to pinpoint the outliers. The robust methods implemented in LIBRA nowadays cover: univariate location, scale (Qn) and skewness estimation (Medcouple), covariance estimation (FAST MCD), regression (FAST-LTS, MCD regression, depth quantiles), principal component analysis (RAPCA, ROBPCA), principal component regression (RPCR), partial least squares regression (RSIMPLS), classification (RDA, RSIMCA) and several methods to deal with skewed data. Besides that, the toolbox contains various methods for cluster analysis, many graphical diagnostic tools, and classical equivalents of several implemented methods. Only a few of the recently added methods will be highlighted in this paper. The features of the LIBRA functions will be illustrated by means of some real data sets. Copyright © 2010 John Wiley & Sons, Inc. For further resources related to this article, please visit the WIREs website.

[1]  Shonda Kuiper,et al.  Introduction to Multiple Regression: How Much Is Your Car Worth? , 2008 .

[2]  Peter J. Rousseeuw,et al.  Robust estimation in very small samples , 2002 .

[3]  Mia Hubert,et al.  An adjusted boxplot for skewed distributions , 2008, Comput. Stat. Data Anal..

[4]  P. Rousseeuw.  Least Median of Squares Regression , 1984 .

[5]  Peter J. Rousseeuw,et al.  Finding Groups in Data: An Introduction to Cluster Analysis , 1990 .

[6]  M. Hubert,et al.  A robust PCR method for high‐dimensional regressors , 2003 .

[7]  M. Hubert,et al.  A fast method for robust principal components with applications to chemometrics , 2002 .

[8]  Mia Hubert,et al.  Fast and robust discriminant analysis , 2004, Comput. Stat. Data Anal..

[9]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[10]  Peter J. Rousseeuw,et al.  An Algorithm for Positive-Breakdown Regression Based on Concentration Steps , 2000 .

[11]  M. Hubert,et al.  Robust classification in high dimensions based on the SIMCA Method , 2005 .

[12]  Stefan Van Aelst,et al.  Robust Multivariate Regression , 2004, Technometrics.

[13]  M. Hubert,et al.  Robust methods for partial least squares regression , 2003 .

[14]  P. Rousseeuw,et al.  A fast algorithm for the minimum covariance determinant estimator , 1999 .

[15]  P. Rousseeuw,et al.  Displaying a clustering with CLUSPLOT , 1999 .

[16]  P. Rousseeuw,et al.  The Bagplot: A Bivariate Boxplot , 1999 .

[17]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[18]  Mia Hubert,et al.  ROBPCA: A New Approach to Robust Principal Component Analysis , 2005, Technometrics.

[19]  Mia Hubert,et al.  Computational Statistics and Data Analysis Robust Pca for Skewed Data and Its Outlier Map , 2022 .

[20]  V. Yohai,et al.  Robust Statistics: Theory and Methods , 2006 .

[21]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[22]  Mia Hubert,et al.  Censored depth quantiles , 2008, Comput. Stat. Data Anal..

[23]  M. Hubert,et al.  A Robust Measure of Skewness , 2004 .

[24]  Mia Hubert,et al.  LIBRA: a MATLAB library for robust analysis , 2005 .

[25]  M. Hubert,et al.  Outlier detection for skewed data , 2008 .

[26]  P. Rousseeuw,et al.  Alternatives to the Median Absolute Deviation , 1993 .