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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Autor principal: Boente, G.
Otros Autores: Fuentes Rodriguez, Daniela, Sued, M.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Academic Press Inc. 2019
Acceso en línea:Registro en Scopus
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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 
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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 
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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 
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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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