Dispersion operators and resistant second-order functional data analysis

Biometrika

Volumn 99, Issue 4, 2012, Pages 813-832

  Kraus, David ^a   Panaretos, Victor M ^a  

^a EPFL   (Switzerland)

Author keywords

Covariance operator; Karhunen Lo ve expansion; M estimation; Resistant test; Spectral truncation; Two sample testing

Indexed keywords

EID: 84869404935     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/ass037     Document Type: Article

References (35)

1. ADLER, R. J. (1990). An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Institute of Mathematical Statistics Lecture Notes - Monograph Series, 12. Hayward: Institute of Mathematical Statistics
2. AMZALLAG, A., VAILLANT, C., JACOB, M., UNSER, M., BEDNAR, J., KAHN, J. D., DUBOCHET, J., STASIAK, A. & MADDOCKS, J. H. (2006). 3D reconstruction and comparison of shapes of DNA minicircles observed by cryoelectron microscopy. Nucleic Acids Res. 34, e125.
3. ANDERSON, M. J. (2006). Distance-based tests for homogeneity of multivariate dispersions. Biometrics 62, 245-53.
4. BALI, L., BOENTE, G., TYLER, D. E. & WANG, J.-L. (2012). Robust functional principal components: A projectionpursuit approach. Ann. Statist. 39, 2852-82.
5. BENKO, M., ḦARDLE, W. & KNEIP, A. (2009). Common functional principal components. Ann. Statist. 37, 1-34.
6. BOENTE, G. & FRAIMAN, R. (1999). Comment on a paper by Locantore et al. Test 8, 28-35.
7. BOENTE, G., RODRIGUEZ, D. & SUED, M. (2011). Testing the equality of covariance operators. In Recent Advances in Functional Data Analysis and Related Topics, Ed. F. Ferraty, pp. 49-53. Heidelberg: Physica-Verlag
8. BOSQ, D. (2000). Linear Processes in Function Spaces: Theory and Applications. New York: Springer
9. BOX, G. E. P. (1953). Non-normality and tests on variances. Biometrika 40, 318-35.
10. CHAUDHURI, P. (1996). On a geometric notion of quantiles for multivariate data. J. Am. Statist. Assoc. 91, 862-72.
11. DAUXOIS, J., POUSSE, A. & ROMAIN, Y. (1982). Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference. J. Mult. Anal. 12, 136-54.
12. FRITZ, H., FILZMOSER, P. & CROUX, C. (2012). A comparison of algorithms for the multivariate L1-median. Comp. Statist., to appear. doi: 10.1007/s00180-011-0262-4.
13. GABRYS, R. & KOKOSZKA, P. (2007). Portmanteau test of independence for functional observations. J. Am. Statist. Assoc. 102, 1338-48.
14. GERVINI, D (2006). Free-knot spline smoothing for functional data. J. R. Statist. Soc. B 68, 671-87.
15. GERVINI, D. (2008). Robust functional estimation using the median and spherical principal components. Biometrika 95, 587-600.
16. HALL, P. & HOSSEINI-NASAB, M. (2006). On properties of functional principal components analysis. J. R. Statist. Soc. B 68, 109-26. (Pubitemid 43415338)
17. HALL, P.,M̈ULLER, H.-G.&WANG, J.-L. (2006). Properties of principal component methods for functional and longitudinal data analysis. Ann. Statist. 34, 1493-517. (Pubitemid 44231170)
18. Wiley HAMPEL, F. R., RONCHETTI, E. M., ROUSSEEUW, P. J. & STAHEL, W. A. (1986). Robust ics. New York: Wiley
19. HORV́ATH, L., HUSKOV́A, M. & KOKOSZKA, P. (2010). Testing the stability of the functional autoregressive process.J. Mult. Anal. 101, 352-67.
20. HUBER, P. J. & RONCHETTI, E. M. (2009). Robust Statistics. Hoboken: Wiley
21. LAYARD, M. W. J. (1974). A Monte Carlo comparison of tests for equality of convariance matrices. Biometrika 61, 461-5.
22. LI, G. & CHEN, Z. (1985). Projection-pursuit approach to robust dispersion matrices and principal components: Primary theory and Monte Carlo. J. Am. Statist. Assoc. 80, 759-66.
23. LOCANTORE, N.,MARRON, J. S., SIMPSON, D. G., TRIPOLI, N., ZHANG, J. T. & COHEN, K. L. (1999). Robust principal component analysis for functional data. Test 8, 1-73.
24. MARDEN, J. I. (1999). Some robust estimates of principal components. Statist. Prob. Lett. 43, 349-59.
25. O'BRIEN, P. C. (1992). Robust procedures for testing equality of covariance matrices. Biometrics 48, 819-27.
26. OLSON, C. L. (1974). Comparative robustness of six tests in multivariate analysis of variance. J. Am. Statist. Assoc. 69, 894-08.
27. PANARETOS, V. M., KRAUS, D. & MADDOCKS, J. H. (2010). Second-order comparison of Gaussian random functions and the geometry of DNA minicircles. J. Am. Statist. Assoc. 105, 670-82.
28. R DEVELOPMENT CORE TEAM (2012). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0, http://www.R-project.org
29. Ramsay J., Silverman B.W. 2005 Functional Data Analysis New York: Springer
30. SERFLING, R. (2004). Nonparametric multivariate descriptive measures based on spatial quantiles. J. Statist. Plan. Infer. 123, 259-78.
31. SIRKI ̈A, S., TASKINEN, S., OJA, H. & TYLER, D. E. (2009). Tests and estimates of shape based on spatial signs and ranks. J. Nonparam. Statist. 21, 155-76.
32. SUN, Y. & GENTON, M. G. (2011). Functional boxplots. J. Comp. Graph. Statist. 20, 316-334.
33. TIKU, M. L. & BALAKRISHNAN, N. (1985). Testing the equality of variance-covariance matrices the robust way. Commun. Statist. A 14, 3033-51.
34. YAO, F. & LEE, T. C. M. (2006). Penalized spline models for functional principal component analysis. J. R. Statist. Soc. B 68, 3-25. (Pubitemid 43415333)
35. ZHANG, J., PANTULA, S. G. & BOOS, D. D. (1991). Robustmethods for testing the pattern of a single covariancematrix. Biometrika 78, 787-95.