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Title: A geometric approach for computing tolerance bounds for elastic functional data

Abstract

We design an approach for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which parsimoniously characterizes variability in the baseline data. Based on the proposed model, we define two different types of tolerance bounds that are able to measure both types of variability, and as a result, identify when the data has gone beyond the bounds of amplitude and/or phase. The first functional tolerance bounds are computed via a bootstrap procedure on the geometric space of amplitude and phase functions. The second functional tolerance bounds utilize functional Principal Component Analysis to construct a tolerance factor. Our report is motivated by two main applications: process control and disease monitoring. The problem of statistical analysis and modeling of functional data in process control is important in determining when a production has moved beyond a baseline. Moreover, in biomedical applications, doctors use long, approximately periodic signals (such as the electrocardiogram) to diagnose and monitor diseases. In this context, it is desirable to identify abnormalities in these signals. We additionally consider a simulated example to assess our approach and compare it to two existing methods.

Authors:
ORCiD logo [1];  [1];  [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. The Ohio State Univ., Columbus, OH (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); National Technical Nuclear Forensics Center (NTNFC)
OSTI Identifier:
1559543
Report Number(s):
SAND-2018-0108J
Journal ID: ISSN 0266-4763; 659761
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Applied Statistics
Additional Journal Information:
Journal Name: Journal of Applied Statistics; Journal ID: ISSN 0266-4763
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Compositional noise; functional data analysis; functional tolerance bounds; functional Principal Component Analysis

Citation Formats

Tucker, J. Derek, Lewis, John R., King, Caleb, and Kurtek, Sebastian. A geometric approach for computing tolerance bounds for elastic functional data. United States: N. p., 2019. Web. doi:10.1080/02664763.2019.1645818.
Tucker, J. Derek, Lewis, John R., King, Caleb, & Kurtek, Sebastian. A geometric approach for computing tolerance bounds for elastic functional data. United States. doi:10.1080/02664763.2019.1645818.
Tucker, J. Derek, Lewis, John R., King, Caleb, and Kurtek, Sebastian. Tue . "A geometric approach for computing tolerance bounds for elastic functional data". United States. doi:10.1080/02664763.2019.1645818.
@article{osti_1559543,
title = {A geometric approach for computing tolerance bounds for elastic functional data},
author = {Tucker, J. Derek and Lewis, John R. and King, Caleb and Kurtek, Sebastian},
abstractNote = {We design an approach for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which parsimoniously characterizes variability in the baseline data. Based on the proposed model, we define two different types of tolerance bounds that are able to measure both types of variability, and as a result, identify when the data has gone beyond the bounds of amplitude and/or phase. The first functional tolerance bounds are computed via a bootstrap procedure on the geometric space of amplitude and phase functions. The second functional tolerance bounds utilize functional Principal Component Analysis to construct a tolerance factor. Our report is motivated by two main applications: process control and disease monitoring. The problem of statistical analysis and modeling of functional data in process control is important in determining when a production has moved beyond a baseline. Moreover, in biomedical applications, doctors use long, approximately periodic signals (such as the electrocardiogram) to diagnose and monitor diseases. In this context, it is desirable to identify abnormalities in these signals. We additionally consider a simulated example to assess our approach and compare it to two existing methods.},
doi = {10.1080/02664763.2019.1645818},
journal = {Journal of Applied Statistics},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {7}
}

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