A half-graph depth for functional data

Sara López Pintado

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: A recent and highly attractive area of research in statistics is the analysis of functional data. In this paper a new definition of depth for functional observations is introduced based on the notion of "half-graph" of a curve. It has computational advantages with respect to other concepts of depth previously proposed. The half-graph depth provides a natural criterion to measure the centrality of a function within a sample of curves. Based on this depth a sample of curves can be ordered from the center outward and L-statistics are defined. The properties of the half-graph depth, such as the 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.

Date: 2005-04
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:ws051603

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