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A half-graph depth for functional data

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  • López Pintado, Sara
  • Romo, Juan

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.

Suggested Citation

  • López Pintado, Sara & Romo, Juan, 2005. "A half-graph depth for functional data," DES - Working Papers. Statistics and Econometrics. WS ws051603, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws051603
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    1. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
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    Cited by:

    1. Franco Pereira, Alba María & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2010. "Comparing quantile residual life functions by confidence bands," DES - Working Papers. Statistics and Econometrics. WS ws103016, Universidad Carlos III de Madrid. Departamento de Estadística.

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