The spatial sign covariance operator: Asymptotic results and applications
Due to increased recording capability, functional data analysis has become an important research topic. For functional data, the study of outlier detection and/or the development of robust statistical procedures started only recently. One robust alternative to the sample covariance operator is the s...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Academic Press Inc.
2019
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| LEADER | 08630caa a22007457a 4500 | ||
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| 001 | PAPER-25640 | ||
| 003 | AR-BaUEN | ||
| 005 | 20250915104249.0 | ||
| 008 | 190410s2019 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85055093414 | |
| 030 | |a JMVAA | ||
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Boente, G. | |
| 245 | 1 | 4 | |a The spatial sign covariance operator: Asymptotic results and applications |
| 260 | |b Academic Press Inc. |c 2019 | ||
| 270 | 1 | 0 | |m Boente, G.; Departamento de Matemáticas, FCEyN, UBA, Ciudad Universitaria, Pabellón 1, Buenos Aires, C1428EHA, Argentina; email: gboente@dm.uba.ar |
| 504 | |a Bali, J., Boente, G., Principal points and elliptical distributions from the multivariate setting to the functional case (2009) Statist. Probab. Lett., 79, pp. 1858-1865 | ||
| 504 | |a Bali, J., Boente, G., Tyler, D., Wang, J., Robust functional principal components: A projection-pursuit approach (2011) Ann. Statist., 39, pp. 2852-2882 | ||
| 504 | |a Benko, M., Härdle, W.K., Kneip, A., Common functional principal components (2009) Ann. Statist., 37, pp. 1-34 | ||
| 504 | |a Boente, G., Rodriguez, D., Sued, M., Testing equality of several covariance operators (2018) Ann. Inst. Statist. Math., 70, pp. 19-950 | ||
| 504 | |a Boente, G., Rodriguez, D., Sued, M., The spatial sign covariance operator: Asymptotic results and applications Available at (2018); Boente, G., Salibian-Barrera, M., S-estimators for functional principal component analysis (2015) J. Amer. Statist. Assoc., 110, pp. 1100-1111 | ||
| 504 | |a Boente, G., Salibian-Barrera, M., Tyler, D., A characterization of elliptical distributions and some optimality properties of principal components for functional data (2014) J. Multivariate Anal., 131, pp. 254-264 | ||
| 504 | |a Cardot, H., Cénac, P., Zitt, P., Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm (2013) Bernoulli, 19, pp. 18-431 | ||
| 504 | |a Cuevas, A., A partial overview of the theory of statistics with functional data (2014) J. Statist. Plann. Inference, 147, pp. 1-23 | ||
| 504 | |a Cuevas, A., Febrero, M., Fraiman, R., Robust estimation and classification for functional data via projection-based depth notions (2007) Comput. Statist., 22, pp. 481-496 | ||
| 504 | |a Dauxois, J., Pousse, A., Romain, Y., Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference (1982) J. Multivariate Anal., 12, pp. 136-154 | ||
| 504 | |a Dürre, A., Tyler, D., Vogel, D., On the eigenvalues of the spatial sign covariance matrix in more than two dimensions (2016) Statist. Probab. Lett., 111, pp. 80-85 | ||
| 504 | |a Dürre, A., Vogel, D., Tyler, D., The spatial sign covariance matrix with unknown location (2014) J. Multivariate Anal., 130, pp. 107-117 | ||
| 504 | |a 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; Ferraty, F., Vieu, P., Viguier-Pla, S., Factor-based comparison of groups of curves (2007) Comput. Statist. Data Anal., 51, pp. 4903-4910 | ||
| 504 | |a Fraiman, R., Muñiz, G., Trimmed means for functional data (2001) Test, 10, pp. 419-440 | ||
| 504 | |a Fremdt, S., Steinbach, J., Horváth, L., Kokoszka, P., Testing the equality of covariance operators in functional samples (2013) Scand. J. Stat., 40, pp. 138-152 | ||
| 504 | |a Gervini, D., Robust functional estimation using the median and spherical principal components (2008) Biometrika, 95, pp. 587-600 | ||
| 504 | |a Goia, A., Vieu, P., An introduction to recent advances in high/infinite dimensional statistics (2016) J. Multivariate Anal., 146, pp. 1-6 | ||
| 504 | |a Hall, P., Horowitz, J., Methodology and convergence rates for functional linear regression (2007) Ann. Statist., 35, pp. 70-91 | ||
| 504 | |a 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; Kraus, D., Panaretos, V., Dispersion operators and resistant second-order functional data analysis (2012) Biometrika, 99, pp. 813-832 | ||
| 504 | |a Lee, S., Shin, H., Billor, N., M-type smoothing splines estimators for principal functions (2013) Comput. Statist. Data Anal., 66, pp. 89-100 | ||
| 504 | |a Lian, H., Functional partial linear model (2011) J. Nonparametr. Stat., 23, pp. 115-128 | ||
| 504 | |a Locantore, N., Marron, J., Simpson, D., Tripoli, N., Zhang, J., Cohen, K., Robust principal components for functional data (1999) Test, 8, pp. 1-28 | ||
| 504 | |a López-Pintado, S., Romo, J., Depth-based inference for functional data (2007) Comput. Statist. Data Anal., 51, pp. 4957-4968 | ||
| 504 | |a Panaretos, V., Kraus, D., Maddocks, J., Second-order comparison of Gaussian random functions and the geometry of DNA minicircles (2010) J. Amer. Statist. Assoc., 105, pp. 670-682 | ||
| 504 | |a Pigoli, D., Aston, J., Dryden, I., Secchi, P., Distances and inference for covariance operators (2014) Biometrika, 101, pp. 409-422 | ||
| 504 | |a Ramsay, J.O., Silverman, B.W., Functional Data Analysis (2005), Springer Berlin; Sawant, P., Billor, N., Shin, H., Functional outlier detection with robust functional principal component analysis (2012) Comput. Statist., 27, pp. 83-102 | ||
| 506 | |2 openaire |e Política editorial | ||
| 520 | 3 | |a Due to increased recording capability, functional data analysis has become an important research topic. For functional data, the study of outlier detection and/or the development of robust statistical procedures started only recently. One robust alternative to the sample covariance operator is the sample spatial sign covariance operator. In this paper, we study the asymptotic behavior of the sample spatial sign covariance operator centered at an estimated location. Among possible applications of our results, we derive the asymptotic distribution of the principal directions obtained from the sample spatial sign covariance operator and we develop a testing procedure to detect differences between the scatter operators of two populations. The test performance is illustrated through a Monte Carlo study for small sample sizes. © 2018 Elsevier Inc. |l eng | |
| 536 | |a Detalles de la financiación: Ministerio de Ciencia, Tecnología e Innovación Productiva | ||
| 536 | |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, 20020130100279 | ||
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, PICT 2014-0351, 201-0377 | ||
| 536 | |a Detalles de la financiación: Universidad de Buenos Aires, MTM2016-76969P | ||
| 536 | |a Detalles de la financiación: The authors wish to thank two anonymous referees and the Editor-in-Chief, Christian Genest, for valuable comments which led to an improved version of the original paper. This research was partially supported by Grants PIP 112-201101-00742 from CONICET , PICT 2014-0351 and 201-0377 from ANPCYT , 20020130100279 BA and 20020150200110 BA from the Universidad de Buenos Aires at Argentina and the Spanish Project MTM2016-76969P from the Ministerio de Ciencia e Innovación at Spain . Appendix | ||
| 593 | |a Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Argentina | ||
| 690 | 1 | 0 | |a ASYMPTOTIC DISTRIBUTION |
| 690 | 1 | 0 | |a FISHER-CONSISTENCY |
| 690 | 1 | 0 | |a FUNCTIONAL DATA |
| 690 | 1 | 0 | |a SPATIAL SIGN COVARIANCE OPERATOR |
| 690 | 1 | 0 | |a SPHERICAL PRINCIPAL COMPONENTS |
| 700 | 1 | |a Fuentes Rodriguez, Daniela | |
| 700 | 1 | |a Sued, M. | |
| 773 | 0 | |d Academic Press Inc., 2019 |g v. 170 |h pp. 115-128 |p J. Multivariate Anal. |x 0047259X |w (AR-BaUEN)CENRE-126 |t Journal of Multivariate Analysis | |
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| 856 | 4 | 0 | |u https://doi.org/10.1016/j.jmva.2018.10.002 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_0047259X_v170_n_p115_Boente |y Handle |
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