Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 170, Issue -, Pages 115-128Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2018.10.002
Keywords
Asymptotic distribution; Fisher-consistency; Functional data; Spatial sign covariance operator; Spherical principal components
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Funding
- CONICET [PIP 112-201101-00742]
- ANPCYT [PICT 2014-0351, 201-0377]
- Universidad de Buenos Aires at Argentina [20020130100279BA, 20020150200110BA]
- Spanish Project from Ministerio de Ciencia e Innovacion at Spain [MTM2016-76969P]
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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. (C) 2018 Elsevier Inc. All rights reserved.
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