The statistical analysis of compositional data
The statistical analysis of compositional data
Averaging of Random Sets Based on Their Distance Functions
Journal of Mathematical Imaging and Vision
The random projection method in goodness of fit for functional data
Computational Statistics & Data Analysis
Robust estimation and classification for functional data via projection-based depth notions
Computational Statistics
A Projection Pursuit Algorithm for Exploratory Data Analysis
IEEE Transactions on Computers
On projection-based tests for directional and compositional data
Statistics and Computing
On projection-based tests for directional and compositional data
Statistics and Computing
On local times, density estimation and supervised classification from functional data
Journal of Multivariate Analysis
Quantiles for finite and infinite dimensional data
Journal of Multivariate Analysis
Resistant estimates for high dimensional and functional data based on random projections
Computational Statistics & Data Analysis
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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.