Frequentist, Bayesian and Resampling Estimation of Extremes Based on the Generalized Extreme Value Distribution
Date
2024-09-04
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Abstract
Extreme events occur in science, engineering, finance and many related fields. The generalized extreme value (GEV) distribution is often used to model extreme events. In this thesis, we study the estimation of GEV related parameters and events using three different approaches. The maximum likelihood approach is a frequentist approach, which has a fully developed theory for both estimation and inference subject to the existence of maximum likelihood estimators and expected and/or observed information matrix. The Bayesian approach starts with the likelihood function, chooses appropriate prior distributions for the GEV distribution parameters, and works with the posterior distribution of the parameters for estimation and inference. The resampling approach may or may not use the likelihood function to estimate the GEV parameters, and inference is based on the variations generated from resampling the observed data directly or indirectly and repeating the estimation procedure. All three approaches are well known in the literature, the main contribution of this thesis is, to the best of our knowledge, that the three approaches are studied and compared under the same setup for the first time, and based on extensive comparisons and the criteria used we are able to recommend the parametric resampling approach based on the empirical distribution function (EDF) estimation, with percentile confidence intervals to practitioners to use. The use of the maximum likelihood, Bayesian, and resampling approaches is illustrated through a case study.
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Keywords
Parameter Estimation, Generalized Extreme Value Distribution, Maximum Likelihood Estimation, Bayesian Analysis, Resampling Approach
Citation
Xue, Y. (2024). Frequentist, Bayesian and resampling estimation of extremes based on the generalized extreme value distribution (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.