Analysis and utilization of extreme value theory for conservative overbounding

Jordan Larson, Demoz Gebre-Egziabher

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

Over the last century Extreme Value Theory (EVT) has become an established collection of statistical methods for estimating the tails of distributions in a wide range of academic disciplines. In addition, the practice of over-bounding the tail probabilities, typically using Gaussian distributions, has been developed in recent years for modeling system uncertainty. This paper analyzes and implements the combination of EVT estimation using the Maximum Likelihood Estimator (MLE) and conservative overbounding. Moreover, quantifying the uncertainties of EVT estimation is paramount for successfully constructing overbounds. Our work primarily investigates these uncertainties through Monte Carlo simulations of a variety of distributions. After characterizing these uncertainties, an EVT-based overbounding approach is presented for a simple linear system. The results of this work show that an EVT-based approach can generate conservative overbounds using significantly less data than experiments alone.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE/ION Position, Location and Navigation Symposium, PLANS 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages462-471
Number of pages10
ISBN (Electronic)9781509020423
DOIs
StatePublished - May 26 2016
EventIEEE/ION Position, Location and Navigation Symposium, PLANS 2016 - Savannah, Georgia
Duration: Apr 11 2016Apr 14 2016

Publication series

NameProceedings of the IEEE/ION Position, Location and Navigation Symposium, PLANS 2016

Other

OtherIEEE/ION Position, Location and Navigation Symposium, PLANS 2016
CountryGeorgia
CitySavannah
Period4/11/164/14/16

Keywords

  • Overbounding
  • certification
  • extreme value theory

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    Larson, J., & Gebre-Egziabher, D. (2016). Analysis and utilization of extreme value theory for conservative overbounding. In Proceedings of the IEEE/ION Position, Location and Navigation Symposium, PLANS 2016 (pp. 462-471). [7479734] (Proceedings of the IEEE/ION Position, Location and Navigation Symposium, PLANS 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/PLANS.2016.7479734