Conservatism Assessment of Extreme Value Theory Overbounds

An approach using extreme value theory (EVT) to generate conservative overbounds for measurement errors is assessed. In this approach, EVT is used to construct a model for tails of an unknown distribution. Results from a Monte Carlo simulation study are presented, which show that estimated tails are not necessarily conservative. The reasons for this lack of conservatism are described and discussed. A method for addressing this lack of conservatism is proposed and evaluated.

[1]  Carl Scarrott,et al.  A Review of Extreme Value Threshold Estimation and Uncertainty Quantification , 2012 .

[2]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  Jonathan A. Tawn,et al.  An extreme-value theory model for dependent observations , 1988 .

[4]  Richard L. Smith Threshold Methods for Sample Extremes , 1984 .

[5]  J. Hosking,et al.  Parameter and quantile estimation for the generalized pareto distribution , 1987 .

[6]  Marc B. Parlange,et al.  STATISTICS OF EXTREMES: MODELING ECOLOGICAL DISTURBANCES , 2005 .

[7]  Hedibert Freitas Lopes,et al.  Data driven estimates for mixtures , 2004, Comput. Stat. Data Anal..

[8]  Demoz Gebre-Egziabher,et al.  Analysis and utilization of extreme value theory for conservative overbounding , 2016, 2016 IEEE/ION Position, Location and Navigation Symposium (PLANS).

[9]  Zuoxiang Peng,et al.  Almost sure convergence for non-stationary random sequences , 2009 .

[10]  Chung-lie Wang Simple Inequalities And Old Limits , 1989 .

[11]  Jean-Marc Azaïs,et al.  EVT-SIAM: A Tool Based on Extreme-Value Theory for the Assessment of SBAS Accuracy and Integrity , 2012 .

[12]  P. Enge,et al.  Paired overbounding and application to GPS augmentation , 2004, PLANS 2004. Position Location and Navigation Symposium (IEEE Cat. No.04CH37556).

[13]  G. W. Pulford,et al.  A Proof of the Spherically Symmetric Overbounding Theorem For Linear Systems , 2008 .

[14]  Bruce DeCleene,et al.  Defining Pseudorange Integrity - Overbounding , 2000 .

[15]  S. Kotz,et al.  Parameter estimation of the generalized Pareto distribution—Part II , 2010 .

[16]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .

[17]  L. H. C. Tippett,et al.  Some Applications of Statistical Methods to the Study of Variation of Quality in the Production of Cotton Yarn , 1935 .

[18]  Sandra Verhagen,et al.  Empirical Integrity Verification of GNSS and SBAS Based on the Extreme Value Theory , 2014 .

[19]  Richard L. Smith Extreme value theory based on the r largest annual events , 1986 .

[20]  Demoz Gebre-Egziabher,et al.  Symmetric overbounding of correlated errors , 2006 .

[21]  L. Haan,et al.  Residual Life Time at Great Age , 1974 .

[22]  J. Pickands Statistical Inference Using Extreme Order Statistics , 1975 .