Robust estimation and classification for functional data via projection-based depth notions

Computational Statistics

Volumn 22, Issue 3, 2007, Pages 481-496

  Cuevas, Antonio ^a   Febrero, Manuel ^b   Fraiman, Ricardo ^c  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^c UNIVERSIDAD DE SAN ANDRÉS   (Argentina)

Author keywords

Depth measures; Functional data; Projections method; Supervised classification

Indexed keywords

EID: 36049026510     PISSN: 09434062     EISSN: 16139658     Source Type: Journal    
DOI: 10.1007/s00180-007-0053-0     Document Type: Article

References (26)

1. Biau G, Bunea F, Wegkamp M (2005) Functional classification in Hilbert spaces. IEEE Trans Inf Theory 51:2163-2172
2. Cérou F, Guyader A (2005) Nearest neighbor classification in infinite dimension. Preprint
3. Cuesta-Albertos JA, Fraiman R, Ransford T (2006a) A sharp form of the Cramer-Wold theorem. J Theor Probab (in press)
4. Cuesta-Albertos JA, Fraiman R, Ransford T (2006b) Random projections and goodness-of-fit tests in infinite-dimensional spaces. Boletim da Sociedade Brasileira de Matematica 37:1-25
5. Cuevas A, Febrero M, Fraiman R (2006) On the use of the bootstrap for estimating functions with functional data. Comput Stat Data Anal 51:1063-1074
6. Devroye L, Györfi L, Lugosi G (1996) A probabilistic theory of pattern recognition. Springer, Heidelberg
7. Donoho DL (1982) Breakdown properties of multivariate location estimators. Ph.D. qualifying paper, Dept. Statist., Harvard University
8. Ferraty F, Vieu P (2003) Curves discrimination: a nonparametric functional approach. Comput Stat Data Anal 44:161-173
9. Ferraty F, Vieu P (2006) Nonparametric modelling for functional data. Springer, Heidelberg
10. Fishman GS (1996) Monte Carlo: concepts, algorithms and applications. Springer, Heidelberg
11. Fraiman R, Meloche J (1999) Multivariate L-estimation. Test 8:255-317
12. Fraiman R, Muniz G (2001) Trimmed means for functional data. Test 10:419-440
13. Ghosh AK, Chaudhuri P (2005) On data depth and distribution-free discriminant analysis using separating surfaces. Bernoulli 11:1-27
14. Hastie T, Buja A, Tibshirani R (1995) Penalized discriminant analysis. Ann Stat 23:73-102
15. Hastie T, Tibshirani R, Friedman J (2001) The elements of statistical learning. Data mining, inference, and prediction. Springer, New York
16. James GM, Hastie TJ (2001) Functional linear discriminant analysis for irregularly sampled curves. J R Stat Soc B 63:533-550
17. Liu RY (1990) On a notion of data depth based on random simplices. Ann Stat 18:405-414
18. Liu RY, Parelius JM, Singh K (1999) Multivariate analysis by data depth: descriptive statistics, graphics and inference. With discussion and a reply by the authors. Ann Stat 27:783-858
19. Ramsay JO, Silverman BW (2002) Applied functional data analysis. Methods and case studies. Springer, New York
20. Ramsay JO, Silverman BW (2005a) Applied functional data analysis. Springer, Heidelberg
21. Ramsay JO, Silverman BW (2005b) Functional data analysis, 2nd edn. Springer, Heidelberg
22. Rousseeuw PJ, Hubert M (1999) Regression depth (with discussion). J Am Stat Assoc 94:388-433
23. Stone CJ (1977) Consistent nonparametric regression. With discussion and a reply by the author. Ann Stat 5:595-645
24. Tukey JW (1975) Mathematics and the picturing of data. In: Proceedings of the International Congress of Mathematicians, pp 523-531. Canad. Math. Congress, Montreal
25. Zuo Y (2003) Projection based depth functions and associated medians. Ann Stat 31:1460-1490
26. Zuo Y, Serfling R (2000) General notions of statistical depth function. Ann Stat 28:461-482