CONICET | Buscador de Institutos y Recursos Humanos

Due to increased recording capability, functional data analysis has become an importantresearch topic. For functional data, the study of outlier detection and/or the developmentof robust statistical procedures started only recently. One robust alternative to the samplecovariance operator is the sample spatial sign covariance operator. In this paper, we studythe asymptotic behavior of the sample spatial sign covariance operator centered at anestimated location. Among possible applications of our results, we derive the asymptoticdistribution of the principal directions obtained from the sample spatial sign covarianceoperator and we develop a testing procedure to detect differences between the scatteroperators of two populations. The test performance is illustrated through a Monte Carlostudy for small sample sizes.