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An Object-Oriented Framework for Robust Multivariate Analysis

  • Valentin Todorov
  • Peter Filzmoser

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 ()
Pages:

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Handle: RePEc:jss:jstsof:32:i03
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  1. Valentin Todorov, 2007. "Robust selection of variables in linear discriminant analysis," Statistical Methods and Applications, Springer, vol. 15(3), pages 395-407, February.
  2. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, 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. 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.
  5. 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.
  6. 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.
  7. Arnold Stromberg, . "Why Write Statistical Software? The Case of Robust Statistical Methods," Journal of Statistical Software, American Statistical Association, vol. 10(i05).
  8. 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.
  9. Stephan Morgenthaler, 2007. "A survey of robust statistics," Statistical Methods and Applications, Springer, vol. 15(3), pages 271-293, February.
  10. 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.
  11. 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.
  12. 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.
  13. Stephan Morgenthaler, 2007. "A survey of robust statistics," Statistical Methods and Applications, Springer, vol. 16(1), pages 171-172, June.
  14. 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.
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