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Abstract:

In this paper, we propose robust estimators for the first canonical correlation and directions of random elements on Hilbert separable spaces by combining sieves and robust association measures, leading to Fisher-consistent estimators for appropriate choices of the association measure. Under regularity conditions, the resulting estimators are consistent. The robust procedure allows us to construct detection rules to identify possible influential observations. The finite sample performance is illustrated through a simulation study in which contaminated data is included. The benefits of considering robust estimators are also illustrated on a real data set where the detection methods reveal the presence of influential observations for the first canonical directions that would be missed otherwise. © 2018 Elsevier Inc.

Registro:

Documento: Artículo
Título:Robust sieve estimators for functional canonical correlation analysis
Autor:Alvarez, A.; Boente, G.; Kudraszow, N.
Filiación:Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
CONICET, Argentina
Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina
Palabras clave:Canonical correlation; Fisher-consistency; Functional data; Robust estimation; Sieves
Año:2019
Volumen:170
Página de inicio:46
Página de fin:62
DOI: http://dx.doi.org/10.1016/j.jmva.2018.03.003
Título revista:Journal of Multivariate Analysis
Título revista abreviado:J. Multivariate Anal.
ISSN:0047259X
CODEN:JMVAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v170_n_p46_Alvarez

Referencias:

  • Alfons, A., Croux, C., Filzmoser, P., Robust maximum association between data sets: The R package ccaPP (2016) Austral. J. Statist., 45, pp. 71-79
  • Alfons, A., Croux, C., Filzmoser, P., Robust maximum association estimators (2017) J. Amer. Statist. Assoc., 112, pp. 436-445
  • Alvarez, A., Métodos Robustos En Correlación Canónica Funcional (2017), http://cms.dm.uba.ar/academico/carreras/doctorado/tesisAlvarez.pdf, (Ph.D. thesis) Universidad de Buenos Aires (in spanish), Available at; Aneiros, G., Bongiorno, E.G., Cao, R., Vieu, P., Functional Statistics and Related Fields (2017), Springer New York; Baillo, A., Cuevas, A., Fraiman, R., Classification methods for functional data (2011) The Oxford Handbook of Functional Data Analysis, pp. 259-297. , Ferraty F. Romain Y. Oxford University Press
  • Bali, L., Boente, G., Principal points and elliptical distributions from the multivariate setting to the functional case (2009) Statist. Probab. Lett., 79, pp. 1858-1865
  • Boente, G., Salibián-Barrera, M., S−estimators for functional principal component analysis (2015) J. Amer. Statist. Assoc., 110, pp. 1100-1111
  • Boente, G., Salibián-Barrera, M., Tyler, D.E., A characterization of elliptical distributions and some optimality properties of principal components for functional data (2014) J. Multivariate Anal., 131, pp. 254-264
  • Branco, J.A., Croux, C., Filzmoser, P., Oliveira, M.R., Robust canonical correlations: A comparative study (2005) Comput. Statist., 20, pp. 203-229
  • Croux, C., Dehon, C., Analyse canonique base sur des estimateurs robustes de la matrice de covariance (2002) La Revue Stat. Appl., 2, pp. 5-26
  • Croux, C., Dehon, C., Influence functions of the Spearman and Kendall correlation measures (2010) Stat. Methods Appl., 9, pp. 497-515
  • Croux, C., Filzmoser, P., (2003), https://lirias.kuleuven.be/bitstream/123456789/118289/1/OR_0341.pdf, Projection pursuit based measures of association. Research report 0341, Katholieke Universiteit Leuven. Available at; Croux, C., Ruiz-Gazen, A., A fast algorithm for robust principal components based on projection pursuit (1996) Compstat: Proceedings in Computational Statistics, pp. 211-217. , Prat A. Physica-Verlag Heidelberg
  • Cuevas, A., A partial overview of the theory of statistics with functional data (2014) J. Statist. Plann. Inference, 147, pp. 1-23
  • Cuevas, A., Febrero, M., Fraiman, R., Robust estimation and classification for functional data via projection-based depth notions (2007) Comput. Statist. Data Anal., 22, pp. 481-496
  • Cupidon, J., Eubank, R., Gilliam, D., Ruymgaart, F., Some properties of canonical correlations and variates in infinite dimensions (2008) J. Multivariate Anal., 99, pp. 1083-1104
  • Cupidon, J., Gilliam, D., Eubank, R., Ruymgaart, F., The delta method for analytic functions of random operators with application to functional data (2007) Bernoulli, 13, pp. 1179-1194
  • Ferraty, F., Romain, Y., The Oxford Handbook of Functional Data Analysis (2010), Oxford University Press; Ferraty, F., Vieu, P., Nonparametric Functional Data Analysis: Theory and Practice (2006), Springer New York; Filzmoser, P., Dehon, C., Croux, C., Outlier resistant estimators for canonical correlation analysis (2000) COMPSTAT: Proceedings in Computational Statistics, pp. 301-306. , Betlehem J.G. van der Heijden P.G.M. Physica-Verlag Heidelberg
  • Gervini, D., Robust functional estimation using the spatial median and spherical principal components (2008) Biometrika, 95, pp. 587-600
  • Goia, A., Vieu, P., An introduction to recent advances in high/infinite dimensional statistics (2016) J. Multivariate Anal., 146, pp. 1-6
  • Hastie, T., Buja, A., Tibshirani, R., Penalized discriminant analysis (1995) Ann. Statist., 23, pp. 73-102
  • He, G., Müller, H.G., Wang, J.L., Extending correlation and regression from multivariate to functional data (2000) Asymptotics in Statistics and Probability, pp. 197-210. , Puri M. VSP Zeist (Netherlands)
  • He, G., Müller, H.G., Wang, J.L., Functional canonical analysis for square integrable stochastic processes (2003) J. Multivariate Anal., 85, pp. 54-77
  • He, G., Müller, H.G., Wang, J.L., Methods of canonical analysis for functional data (2004) J. Statist. Plann. Inference, 122, pp. 141-159
  • He, G., Müller, H.G., Wang, J.L., Yang, W., Functional linear regression via canonical analysis (2010) Bernouilli, 16, pp. 705-729
  • Horváth, L., Kokoszka, P., Inference for Functional Data with Applications (2012), Springer New York; Hsing, T., Eubank, R., Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators (2015), Wiley New York; Hubert, M., Rousseeuw, P., Segaert, P., Multivariate functional outlier detection (2015) Stat. Methods Appl., 24, pp. 177-202
  • Hubert, M., Rousseeuw, P., Segaert, P., Multivariate and functional classification using depth and distance (2017) Adv. Data Anal. Classif., 11, pp. 445-466
  • Hubert, M., Vandervieren, E., An adjusted boxplot for skewed distributions (2008) Comput. Statist. Data Anal., 52, pp. 5186-5201
  • Jin, J., Cui, H., Asymptotic distributions in the projection pursuit based canonical correlation analysis (2010) Sci. China Math., 53, pp. 485-498
  • Karnel, G., Robust canonical correlation and correspondence analysis (1991) The Frontiers of Statistical Scientific and Industrial Applications. Proceedings of ICOSCO-I, Vol. II, pp. 415-420. , American Sciences Press
  • Leurgans, S.E., Moyeed, R.A., Silverman, B.W., Canonical correlation analysis when the data are curves (1993) J. Roy. Statist. Soc. Ser B., 55, pp. 725-740
  • Locantore, N., Marron, J.S., Simpson, D.G., Tripoli, N., Zhang, J.T., Cohen, K.L., Robust principal components for functional data (with discussion) (1999) TEST, 8, pp. 1-73
  • Maronna, R., Robust M−estimators of multivariate location and scatter (1976) Ann. Statist., 4, pp. 51-67
  • Maronna, R., Martin, R.D., Yohai, V., Robust Statistics: Theory and Methods (2006), John Wiley & Sons New York; Maronna, R., Zamar, R., Robust estimates of location and dispersion for high-dimensional datasets (2002) Technometrics, 44, pp. 307-317
  • Ramsay, J.O., Silverman, B.W., Functional Data Analysis (2005), Springer Berlin; Shevlyakov, G.L., Vilchevski, N.O., Robustness in Data Analysis: Criteria and Methods (2001), Walter de Gruyter Utrech; Taskinen, S., Croux, C., Kankainen, A., Ollila, E., Oja, H., Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices (2006) J. Multivariate Anal., 97, pp. 359-384
  • Williams, B., Toussaint, M., Storkey, A., A primitive based generative model to infer timing information in unpartitioned handwriting data (2007), pp. 1119-1124. , Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, M. Veloso (Eds.); Yao, Y., Wu, F., Zou, J., Probability–enhanced effective dimension reduction for classifying sparse functional data (2016) TEST, 25, pp. 1-22
  • Yohai, V.J., Ben, M.G., Canonical variables as optimal predictors (1980) Ann. Statist., 8, pp. 865-869

Citas:

---------- APA ----------
Alvarez, A., Boente, G. & Kudraszow, N. (2019) . Robust sieve estimators for functional canonical correlation analysis. Journal of Multivariate Analysis, 170, 46-62.
http://dx.doi.org/10.1016/j.jmva.2018.03.003
---------- CHICAGO ----------
Alvarez, A., Boente, G., Kudraszow, N. "Robust sieve estimators for functional canonical correlation analysis" . Journal of Multivariate Analysis 170 (2019) : 46-62.
http://dx.doi.org/10.1016/j.jmva.2018.03.003
---------- MLA ----------
Alvarez, A., Boente, G., Kudraszow, N. "Robust sieve estimators for functional canonical correlation analysis" . Journal of Multivariate Analysis, vol. 170, 2019, pp. 46-62.
http://dx.doi.org/10.1016/j.jmva.2018.03.003
---------- VANCOUVER ----------
Alvarez, A., Boente, G., Kudraszow, N. Robust sieve estimators for functional canonical correlation analysis. J. Multivariate Anal. 2019;170:46-62.
http://dx.doi.org/10.1016/j.jmva.2018.03.003