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Activity Number: 31
Type: Contributed
Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #316965 View Presentation
Title: A New Notion of Depth and Central Regions for Functional Data
Author(s): Naveen Narisetty* and Vijay Nair
Companies: University of Michigan and University of Michigan
Keywords:
Abstract:

Multivariate notions of depth play an important role in robust multivariate data analysis. However, relatively less attention has been received by depth notions for functional data. We propose a new notion of functional depth called Extremal Depth (ED), which considers extreme outlyingness of the functional data similar to the projection depth in the multivariate case. We show that ED satisfies many desirable properties as a depth notion and is well suited for obtaining central regions of functional data. For constructing central regions, ED satisfies two important properties that are not shared by other notions: a) the central region achieves the nominal (desired) simultaneous coverage probability; and b) the width of the simultaneous region is proportional to that of the pointwise central regions. The usefulness of ED is demonstrated for constructing functional boxplots and for detecting outliers. Through empirical studies, we show that ED box plots are robust and more effective in detecting outliers compared to existing notions.


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