Robust distances for outlier-free goodness-of-fit testing

Computational Statistics and Data Analysis

Volumn 65, Issue , 2013, Pages 29-45

  Cerioli, Andrea ^a   Farcomeni, Alessio ^b   Riani, Marco ^a  

^a UNIVERSITY OF PARMA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Beta distribution; False discovery rate; Multivariate normality; Outlier removal; Reweighted MCD; Trimming

Indexed keywords

NUMERICAL METHODS; POPULATION STATISTICS; STOCHASTIC SYSTEMS; TRIMMING;

BETA DISTRIBUTIONS; FALSE DISCOVERY RATE; MULTIVARIATE NORMALITY; OUTLIER REMOVALS; REWEIGHTED MCD;

STATISTICS;

EID: 84885022943     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2012.03.008     Document Type: Article

References (38)

1. Alfons, A., Baaske, W.E., Filzmoser, P., Mader, W., Wieser, R., 2011. Robust variable selection with application to quality of life research. Statistical Methods and Applications 20, 65-82.
2. Alvarez-Esteban, P.C., del Barrio, E., Cuesta-Albertos, J.A., Matrán, C., 2010. Assessing when a sample is mostly normal. Computational Statistics and Data Analysis 54, 2914-2925.
3. Atkinson, A.C., Riani, M., Cerioli, A., 2004. Exploring Multivariate Data with the Forward Search. Springer, New York.
4. Beirlant, J., Mason, D.M., Vynckier, C., 1999. Goodness-of-fit analysis for multivariate normality based on generalized quantiles. Computational Statistics and Data Analysis 30, 119-142. (Pubitemid 32262790)
5. Benjamini, Y., Hochberg, Y., 1995. Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society (Series B) 57, 289-300.
6. Bordes, L., Mottelet, S., Vandekerkhove, P., 2006. Semiparametric estimation of a two-component mixture model. The Annals of Statistics 34, 1204-1232. (Pubitemid 44231161)
7. Cerioli, A., 2010a. Multivariate outlier detection with high-breakdown estimators. Journal of the American Statistical Association 105, 147-156.
8. Cerioli, A., 2010b. Diagnostic checking of multivariate normality under contamination. In: Lechevallier, Y., Saporta, G. (Eds.), Proceedings of COMPSTAT'2010. Physica-Verlag, Heidelberg, pp. 871-878.
9. Cerioli, A., Farcomeni, A., 2011. Error rates for multivariate outlier detection. Computational Statistics and Data Analysis 55, 544-553.
10. Cerioli, A., Riani, M., Torti, F., 2012. Size and power of multivariate outlier detection rules. In: Lausen, B., van den Poel, D. and Ultsch, A. (Eds.), Proceedings of GfKl/IFCS 2011, Springer, Berlin (in press).
11. Croux, C., Dehon, C., 2010. Influence functions of the Spearman and Kendall correlation measures. Statistical Methods and Applications 19, 497-515.
12. Croux, C., Haesbroeck, G., 1999. Influence function and efficiency of the minimum covariance determinant scatter matrix estimator. Journal of Multivariate Analysis 71, 161-190.
13. Croux, C., Haesbroeck, G., 2000. Principal components analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies. Biometrika 87, 603-618.
14. Cuesta-Albertos, J.A., Matrán, C., Mayo-Iscar, A., 2008. Trimming and likelihood: robust location and dispersion estimation in the elliptical model. The Annals of Statistics 36, 2284-2318.
15. Farcomeni, A., 2008. A review of modern multiple hypothesis testing, with particular attention to the false discovery proportion. Statistical Methods in Medical Research 17, 347-388.
16. Filzmoser, P., Maronna, R., Werner, M., 2008. Outlier identification in high dimensions. Computational Statistics and Data Analysis 52, 1694-1711. (Pubitemid 350017776)
17. Flury, B., Riedwyl, H., 1988. Multivariate Statistics: A Practical Approach. Chapman and Hall, London.
18. Gallegos, M.T., Ritter, G., 2005. A robust method for cluster analysis. The Annals of Statistics 33, 347-380. (Pubitemid 40653793)
19. Garcìa-Escudero, L.A., Gordaliza, A., 2005. Generalized radius processes for elliptically contoured distributions. Journal of the American Statistical Association 100, 1036-1045. (Pubitemid 41276347)
20. Garcìa-Escudero, L.A., Gordaliza, A., Matrán, C., Mayo-Iscar, A., 2008. A general trimming approach to robust cluster analysis. The Annals of Statistics 36, 1324-1345.
21. Gnanadesikan, R., 1997. Methods for Statistical Data Analysis of Multivariate Observations, second ed. Wiley, New York.
22. Hardin, J., Rocke, D.M., 2005. The distribution of robust distances. Journal of Computational and Graphical Statistics 14, 910-927.
23. Hubert, M., Rousseeuw, P.J., Van Aelst, S., 2008. High-breakdown robust multivariate methods. Statistical Science 23, 92-119.
24. Hubert, M., Van Driessen, K., 2004. Fast and robust discriminant analysis. Computational Statistics and Data Analysis 45, 301-320. (Pubitemid 38204905)
25. Hunter, D.R., Wang, S., Hettmansperger, T.P., 2007. Inference for mixtures of symmetric distributions. The Annals of Statistics 35, 224-251.
26. Koziol, J.A., 1982. A class of invariant procedures for assessing multivariate normality. Biometrika 69, 423-427.
27. Lopuhaä, H.P., 1999. Asymptotics of reweighted estimators of multivariate location and scatter. The Annals of Statistics 27, 1638-1665.
28. Maronna, R.A., Martin, R.D., Yohai, V.J., 2006. Robust Statistics: Theory and Methods. Wiley, Chichester.
29. Mecklin, C.J., Mundfrom, D.J., 2004. An appraisal and bibliography of tests for multivariate normality. International Statistical Review 72, 123-138. (Pubitemid 38845755)
30. Moore, D.S., Stubblebine, J.B., 1981. Chi-square tests for multivariate normality with application to common stock prices. Communications in Statistics - Theory and Methods A 10, 713-738.
31. Riani, M., Atkinson, A.C., Cerioli, A., 2009. Finding an unknown number of multivariate outliers. Journal of the Royal Statistical Society (Series B) 71, 447-466.
32. Rousseeuw, P.J., Van Aelst, S., Van Driessen, K., Agullò, J., 2004. Robust multivariate regression. Technometrics 46, 293-305.
33. Scheffé, H., 1959. The Analysis of Variance. Wiley, New York.
34. Singh, A., 1993. Omnibus robust procedures for assessment of multivariate normality and detection of multivariate outliers. In: Patil, G.P., Rao, C.R. (Eds.), Multivariate Environmental Statistics. Elsevier, pp. 445-488.
35. Todorov, V., Filzmoser, P., 2009. An object-oriented framework for robust multivariate analysis. Journal of Statistical Software 32, 1-47.
36. Van Aelst, S., Vandervieren, E., Willems, G., 2012. A Stahel-Donoho estimator based on huberized outlyingness. Computational Statistics and Data Analysis 56, 531-542.
37. Van Aelst, S., Willems, G., 2011. Robust and efficient one-way MANOVA tests. Journal of the American Statistical Association 106, 706-718.
38. Willems, G., Joe, H., Zamar, R., 2009. Diagnosing multivariate outliers detected by robust estimators. Journal of Computational and Graphical Statistics 18, 73-91.