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An Object-Oriented Framework for Robust Multivariate Analysis

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  • Valentin Todorov
  • Peter Filzmoser

Abstract

Taking advantage of the S4 class system of the programming environment R, which facilitates the creation and maintenance of reusable and modular components, an object-oriented framework for robust multivariate analysis was developed. The framework resides in the packages robustbase and rrcov and includes an almost complete set of algorithms for computing robust multivariate location and scatter, various robust methods for principal component analysis as well as robust linear and quadratic discriminant analysis. The design of these methods follows common patterns which we call statistical design patterns in analogy to the design patterns widely used in software engineering. The application of the framework to data analysis as well as possible extensions by the development of new methods is demonstrated on examples which themselves are part of the package rrcov.

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Article provided by American Statistical Association in its journal Journal of Statistical Software.

Volume (Year): 32 ()
Issue (Month): i03 ()
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Handle: RePEc:jss:jstsof:32:i03

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  1. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
  2. Todorov, Valentin & Neykov, Neyko & Neytchev, Plamen, 1994. "Robust two-group discrimination by bounded influence regression. A Monte Carlo simulation," Computational Statistics & Data Analysis, Elsevier, vol. 17(3), pages 289-302, March.
  3. Todorov, Valentin & Filzmoser, Peter, 2010. "Robust statistic for the one-way MANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 37-48, January.
  4. Abul Naga, Ramses & Antille, Gerard, 1990. "Stability of robust and non-robust principal components analysis," Computational Statistics & Data Analysis, Elsevier, vol. 10(2), pages 169-174, October.
  5. Hawkins, Douglas M., 1994. "The feasible solution algorithm for the minimum covariance determinant estimator in multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 197-210, February.
  6. Stephan Morgenthaler, 2007. "A survey of robust statistics," Statistical Methods and Applications, Springer, vol. 16(1), pages 171-172, June.
  7. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
  8. He, Xuming & Fung, Wing K., 2000. "High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 151-162, February.
  9. Valentin Todorov, 2007. "Robust selection of variables in linear discriminant analysis," Statistical Methods and Applications, Springer, vol. 15(3), pages 395-407, February.
  10. Arnold Stromberg, . "Why Write Statistical Software? The Case of Robust Statistical Methods," Journal of Statistical Software, American Statistical Association, vol. 10(i05).
  11. Todorov, Valentin, 1992. "Computing the minimum covariance determinant estimator (MCD) by simulated annealing," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 515-525, November.
  12. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(1), pages 1-73, June.
  13. Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.
  14. Stephan Morgenthaler, 2007. "A survey of robust statistics," Statistical Methods and Applications, Springer, vol. 15(3), pages 271-293, February.
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Cited by:
  1. Marco Riani & Andrea Cerioli & Francesca Torti, 2014. "On consistency factors and efficiency of robust S-estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 23(2), pages 356-387, June.
  2. M. Hubert & P. Rousseeuw & K. Vakili, 2014. "Shape bias of robust covariance estimators: an empirical study," Statistical Papers, Springer, vol. 55(1), pages 15-28, February.
  3. Robert Finger, 2010. "Review of ‘Robustbase’ software for R," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(7), pages 1205-1210, November/.
  4. Matthias Kohl & Peter Ruckdeschel & Helmut Rieder, 2010. "Infinitesimally Robust estimation in general smoothly parametrized models," Statistical Methods and Applications, Springer, vol. 19(3), pages 333-354, August.
  5. Valentin Todorov & Matthias Templ & Peter Filzmoser, 2011. "Detection of multivariate outliers in business survey data with incomplete information," Advances in Data Analysis and Classification, Springer, vol. 5(1), pages 37-56, April.
  6. Sanjeena Subedi & Paul McNicholas, 2014. "Variational Bayes approximations for clustering via mixtures of normal inverse Gaussian distributions," Advances in Data Analysis and Classification, Springer, vol. 8(2), pages 167-193, June.
  7. Katherine Morris & Paul McNicholas & Luca Scrucca, 2013. "Dimension reduction for model-based clustering via mixtures of multivariate $$t$$ t -distributions," Advances in Data Analysis and Classification, Springer, vol. 7(3), pages 321-338, September.
  8. Vakili, Kaveh & Schmitt, Eric, 2014. "Finding multivariate outliers with FastPCS," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 54-66.
  9. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2013. "Robust distances for outlier-free goodness-of-fit testing," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 29-45.
  10. Klaus Nordhausen & Hannu Oja, . "Multivariate L1 Statistical Methods: The Package MNM," Journal of Statistical Software, American Statistical Association, vol. 43(i05).

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