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A Topologically Valid Definition of Depth for Functional Data

Abstract: The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Statistical Science, Vol. 31, Num. 1 (2016), P. 61-79.

Editorial: Institute of Mathematical Statistics (IMS)

 Fecha de publicación: 10/02/2016

Nº de páginas: 19

Tipo de publicación: Artículo de Revista

 DOI: 10.1214/15-STS532

ISSN: 0883-4237,2168-8745

Url de la publicación: http://dx.doi.org/10.1214/15-STS532