A Topologically Valid Definition of Depth for Functional Data

File Description SizeFormat 
euclid.ss.1455115914.pdfPublished version359.02 kBAdobe PDFDownload
Title: A Topologically Valid Definition of Depth for Functional Data
Author(s): Nieto-Reyes, A
Battey, H
Item Type: Journal Article
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.
Publication Date: 10-Feb-2016
Date of Acceptance: 1-Feb-2016
URI: http://hdl.handle.net/10044/1/41332
DOI: http://dx.doi.org/10.1214/15-STS532
ISSN: 0883-4237
Publisher: Project Euclid
Start Page: 61
End Page: 79
Journal / Book Title: Statistical Science
Volume: 31
Issue: 1
Copyright Statement: © Institute of Mathematical Statistics, 2016
Keywords: Statistics & Probability
0104 Statistics
Publication Status: Published
Appears in Collections:Mathematics

Items in Spiral are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commons