JSM 2015 Preliminary Program

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Activity Number: 66
Type: Topic Contributed
Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #315847 View Presentation
Title: Extremal Notion of Depth for Functional Data with Applications to Simultaneous Inference
Author(s): Naveen Narisetty* and Vijay Nair
Companies: University of Michigan and University of Michigan
Keywords:
Abstract:

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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