A half-region depth for functional data

Sara López-Pintado and Juan Romo

Computational Statistics & Data Analysis, 2011, vol. 55, issue 4, 1679-1695

Abstract: 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.

Keywords: Functional; data; Data; depth; Order; statistics; High-dimensional; data (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (25)

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