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On depth measures and dual statistics. A methodology for dealing with general data. (English) Zbl 1163.62039
J. Multivariate Anal. 100, No. 4, 753-766 (2009); corrigendum ibid. 112, 256 (2012).
Summary: A general depth measure, based on the use of one-dimensional linear continuous projections, is proposed. The applicability of this idea in different statistical setups (including inference in functional data analysis, image analysis and classification) is discussed. A special emphasis is made on the possible usefulness of this method in some statistical problems where the data are elements of a Banach space.
The asymptotic properties of the empirical approximation of the proposed depth measure are investigated. In particular, its asymptotic distribution is obtained through \(U\)-statistics techniques. The practical aspects of these ideas are discussed through a small simulation study and a real-data example.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
46N30 Applications of functional analysis in probability theory and statistics
62E20 Asymptotic distribution theory in statistics
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62H35 Image analysis in multivariate analysis
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