Depth-based inference for functional data
Computational Statistics & Data Analysis
Editorial: Statistics for Functional Data
Computational Statistics & Data Analysis
Robust estimation and classification for functional data via projection-based depth notions
Computational Statistics
Computational Statistics & Data Analysis
On the use of the bootstrap for estimating functions with functional data
Computational Statistics & Data Analysis
Functional data analysis in shape analysis
Computational Statistics & Data Analysis
Supervised classification for functional data: A weighted distance approach
Computational Statistics & Data Analysis
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A new definition of depth for functional observations is introduced based on the notion of ''half-region'' determined by a curve. The half-region depth provides a simple and natural criterion to measure the centrality of a function within a sample of curves. It has computational advantages relative to other concepts of depth previously proposed in the literature which makes it applicable to the analysis of high-dimensional data. Based on this depth a sample of curves can be ordered from the center-outward and order statistics can be defined. The properties of the half-region depth, such as consistency and uniform convergence, are established. A simulation study shows the robustness of this new definition of depth when the curves are contaminated. Finally, real data examples are analyzed.