Abstract Details
Activity Number:
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66
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Type:
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Topic Contributed
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Date/Time:
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Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #315847
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View Presentation
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Title:
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Extremal Notion of Depth for Functional Data with Applications to Simultaneous Inference
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Author(s):
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Naveen Narisetty* and Vijay Nair
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Companies:
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University of Michigan and University of Michigan
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Keywords:
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Abstract:
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There has been extensive work on data depths and their applications for multivariate data. However, depth notions for infinite-dimensional objects such as functional data have received less attention. We propose a new notion of depth called Extremal Depth (ED) for functional data, discuss its properties, and compare its performance with existing notions. ED has many desirable properties as a measure of depth and is well suited for obtaining central regions of functional data and corresponding regions for distributions on function spaces. We show that the ED central regions are exact in the sense that they achieve nominal (desired) simultaneous coverage probability, a property not shared by existing depth notions. ED notion together with bootstrapping can be used to obtain simultaneous confidence bands for functional parameters of interest in a variety of problems including parametric and nonparametric regression. We show through empirical studies that this gives simultaneous confidence bands that are narrower while achieving the desired coverage.
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Authors who are presenting talks have a * after their name.
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