S-Estimators for Functional Principal Component Analysis

Journal of the American Statistical Association

Volumn 110, Issue 511, 2015, Pages 1100-1111

  Boente, Graciela ^a   Salibian Barrera, Matías ^b  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Functional data analysis; Robust estimation; Sparse data

Indexed keywords

EID: 84946962840     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2014.946991     Document Type: Article

References (41)

1. L.Bali,, G.Boente,, D.Tyler,, J.L.Wang, (2011), Robust Functional Principal Components: A Projection-Pursuit Approach, The Annals of Statistics, 39, 2852–2882.
2. C.Becker,, U.Gather, (2001), The Largest Nonidentifiable Outliers: A Comparison of Multivariate Simultaneous Outliers Identification Rules, Computational Statistics and Data Analysis, 36, 119–127.
3. G.Boente, (1987), Asymptotic Theory for Robust Principal Components, Journal of Multivariate Analysis, 21, 67–78.
4. G.Boente,, M.Salibian-Barrera,, D.Tyler, (2014), A Characterization of Elliptical Distributions and Some Optimality Properties of Principal Components for Functional Data, Journal of Multivariate Analysis, 131, 254–264.
5. N.A.Campbell, (1980), Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation, Applied Statistics, 29, 231–237.
6. E.J.Candès,, X.Li,, Y.Ma,, J.Wright, (2011), Robust Principal Component Analysis? Journal of the ACM, 58, 1–37.
7. V.Chandrasekaran,, S.Sanghavi,, P.Parrilo,, A.S.Willsky, (2011), Rank-Sparsity Incoherence for Matrix Decomposition, SIAM Journal of Optimization, 21, 572–596.
8. C.Croux,, P.Filzmoser,, G.Pison,, P.J.Rousseeuw, (2003), Fitting Multiplicative Models by Robust Alternating Regressions, Statistics and Computing, 13, 23–36.
9. C.Croux,, G.Haesbroeck, (2000), Principal Component Analysis Based on Robust Estimators of the Covariance or Correlation Matrix: Influence Functions and Efficiencies, Biometrika, 87, 603–618.
10. C.Croux,, and A.Ruiz-Gazen, (1996), “A Fast Algorithm for Robust Principal Components Based on Projection Pursuit,” in Compstat: Proceedings in Computational Statistics, ed. A. Prat, Heidelberg: Physica-Verlag, pp. 211–216.
11. C.Croux, (2005), High-Breakdown Estimators for Principal Components: The Projection-Pursuit Approach Revisited, Journal of Multivariate Analysis, 95, 206–226.
12. H.Cui,, X.He,, K.W.Ng, (2003), Asymptotic Distribution of Principal Components Based on Robust Dispersions, Biometrika, 90, 953–966.
13. F.Torre,, M.J.Black, (2001), Robust Principal Components Analysis for Computer Vision, Proceedings of the 8th International Conference on Computer Vision, 1,. 362–369.
14. S.J.Devlin,, R.Gnanadesikan,, J.R.Kettenring, (1981), Robust Estimation of Dispersion Matrices and Principal Components, Journal of the American Statistical Association, 76, 354–362.
15. M.Febrero,, P.Galeano,, W.Gonzalez-Manteiga, (2007), A Functional Analysis of NOx Levels: Location and Scale Estimation and Outlier Detection, Computational Statistics, 22, 411–427.
16. M.Febrero, (2008), Outlier Detection in Functional Data by Depth Measures, With Application to Identify Abnormal Nox Levels, Environmetrics, 19, 331–345.
17. D.Gervini, (2008), Robust Functional Estimation Using the Spatial Median and Spherical Principal Components, Biometrika, 95, 587–600.
18. J.Hardin,, D.Rocke, (2005), The Distribution of Robust Distances, Journal of Computational and Graphical Statistics, 14, 1–19.
19. P.J.Huber,, and E.M.Ronchetti, (2009), Robust Statistics (2nd ed.), New York: Wiley.
20. M.Hubert,, P.J.Rousseeuw,, K.Branden, (2005), ROBPCA: A New Approach to Robust Principal Component Analysis, Technometrics, 47, 64–79.
21. M.Hubert,, P.J.Rousseeuw,, S.Verboven, (2002), A Fast Method for Robust Principal Components With Applications to Chemometrics, Chemometrics and Intelligent Laboratory Systems, 60, 101–111.
22. M.Hubert,, E.Vandervieren, (2008), An Adjusted Boxplot for Skewed Distributions, Computational Statistics and Data Analysis, 52, 5186–5201.
23. R.J.Hyndman,, S.Ullah, (2007), Robust Forecasting of mortality and Fertility Rates: A Functional Data Approach, Computational Statistics and Data Analysis, 51, 4942–4956.
24. R.J.Hyndman,, H.L.Shang, (2010), Rainbow Plots, Bagplots, and Boxplots for Functional Data, Journal of Computational and Graphical Statistics, 19, 29–45.
25. G.Lerman,, M.McCoy,, J.A.Tropp,, T.Zhang, (2014), Robust Computation of Linear Models, or How to Find a Needle in a Haystack, Foundations of Computational Mathematics, 15, 363–410.
26. G.Li,, Z.Chen, (1985), Projection Pursuit Approach to Robust Dispersion Matrices and Principal Components: Primary Theory and Monte Carlo, Journal of the American Statistical Association, 80, 759–766.
27. L.Liu,, D.Hawkins,, S.Ghosh,, S.Young, (2003), Robust Singular Value Decomposition Analysis of Microarray Data, Proceedings of the National Academy of Sciences, 100,. 13167–13172.
28. N.Locantore,, J.S.Marron,, D.G.Simpson,, N.Tripoli,, J.T.Zhang,, K.L.Cohen, (1999), Robust Principal Components for Functional Data, Test, 8, 1–28.
29. R.Maronna, (2005), Principal Components and Orthogonal Regression Based on Robust Scales, Technometrics, 47, 264–273.
30. R.Maronna,, R.D.Martin,, and V.Yohai, (2006), Robust Statistics: Theory and Methods, Chichester, UK: Wiley.
31. R.Maronna,, V.Yohai, (2008), Robust Lower–Rank Approximation of Data Matrices With Element–Wise Contamination, Technometrics, 50, 295–304.
32. M.McCoy,, J.A.Tropp, (2011), Two Proposals for Robust PCA Using Semidefinite Programming, Electronic Journal of Statistics, 5, 1123–1160.
33. R.Naga,, G.Antille, (1990), Stability of Robust and Non–Robust Principal Component Analysis, Computational Statistics and Data Analysis, 10, 169–174.
34. G.Pison,, S.van Aelst, (2004), Diagnostic Plots for Robust Multivariate Methods, Journal of Computational and Graphical Statistics, 13, 1–20.
35. P.J.Rousseeuw,, K.van Driessen, (1999), A Fast Algorithm for the Minimum Covariance Determinant Estimator, Technometrics, 41, 212–223.
36. P.J.Rousseeuw,, B.C.Van Zomeren, (1990), Unmasking Multivariate Outliers and Leverage Points, Journal of the American Statistical Association, 85, 633–651.
37. M.Salibian-Barrera,, V.J.Yohai, (2006), A Fast Algorithm for S-Regression Estimates, Journal of Computational and Graphical Statistics, 15, 414–427.
38. P.Sawant,, N.Billor,, H.Shin, (2012), Functional Outlier Detection With Robust Functional Principal Component Analysis, Computational Statistics, 27, 83–102.
39. P.Verboon,, W.J.Heiser, (1994), Resistant Lower-Rank Approximation of Matrices by Iterative Majorization, Computational Statistics and Data Analysis, 18, 457–467.
40. H.Xu,, C.Caramanis,, S.Sanghavi, (2012), Robust PCA via Outlier Pursuit, IEEE Transactions on Information Theory, 58, 3047–3064.
41. T.Zhang,, G.Lerman, (2014), A Novel M-Estimator for Robust PCA, Journal of Machine Learning Research, 15, 749–808.