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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.


Documento: Artículo
Título:The spatial sign covariance operator: Asymptotic results and applications
Autor:Boente, G.; Rodriguez, D.; Sued, M.
Filiación:Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Argentina
Palabras clave:Asymptotic distribution; Fisher-consistency; Functional data; Spatial sign covariance operator; Spherical principal components
Página de inicio:115
Página de fin:128
Título revista:Journal of Multivariate Analysis
Título revista abreviado:J. Multivariate Anal.


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---------- APA ----------
Boente, G., Rodriguez, D. & Sued, M. (2019) . The spatial sign covariance operator: Asymptotic results and applications. Journal of Multivariate Analysis, 170, 115-128.
---------- CHICAGO ----------
Boente, G., Rodriguez, D., Sued, M. "The spatial sign covariance operator: Asymptotic results and applications" . Journal of Multivariate Analysis 170 (2019) : 115-128.
---------- MLA ----------
Boente, G., Rodriguez, D., Sued, M. "The spatial sign covariance operator: Asymptotic results and applications" . Journal of Multivariate Analysis, vol. 170, 2019, pp. 115-128.
---------- VANCOUVER ----------
Boente, G., Rodriguez, D., Sued, M. The spatial sign covariance operator: Asymptotic results and applications. J. Multivariate Anal. 2019;170:115-128.