Constructing EVT-based confidence bounds using bootstrapping

Certification of new technologies is a challenge today because of the increasing complexity of systems often described as systems of systems. This increase often leads to the need for large amounts of data for statistical analysis of these systems. With this comes the need for improved methods for uncertainty quantification especially with regards to data efficiency. One statistical methodology which holds promise in this regard is Extreme Value Theory (EVT) which states that the tails of distribution functions can be well approximated by a General Pareto Distribution (GPD). The techniques associated with EVT have been used extensively by statisticians in other domains such as insurance and finance, but have not been applied consistently to aerospace applications. The work presented in this paper is part of ongoing efforts in investigating the performance of EVT for conservative estimation of unknown heavy-tailed distributions, that is, the conservative distribution function overbounds the actual underlying distribution which the data is drawn from. Although prior work has shown that EVT is not directly conservative, an estimation approach based on confidence intervals of the GPD model's parameters is currently being assessed for its conservatism. In this paper the commmon statistical practice of bootstrapping data for the construction of confidence intervals is studied and compared to theoretical methods and experimental data for a variety of heavy-tailed distributions. In summary this paper shows that bootstrapping alone is not sufficient to guarantee conservative confidence intervals of the GPD parameters for the construction of an overbounding distribution of the unknown heavy-tailed distribution. The results are in line with the theoretical approach investigated previously.