Discrete Parameter Estimation for Rare Events: From Binomial to Extreme Value Distributions
by Laura Fee Schneider
Date of Examination:2019-04-26
Date of issue:2019-06-13
Advisor:Prof. Dr. Andrea Krajina
Referee:Prof. Dr. Andrea Krajina
Referee:Prof. Dr. Tatyana Krivobokova
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Abstract
English
Estimating a discrete parameter from rare events is a challenging task, since observations are scarce in such situations. In this cumulative dissertation two distinct problems resulting from rare events are discussed and methodologies to solve them are suggested. First, we employ a Bayesian approach in the binomial model to overcome a lack of information on the parameter n that arises from a small success probability. In this demanding setting we derive a posterior consistency statement that delivers a clearer theoretical understanding for the asymptotic behaviour of Bayesian estimators. Secondly, we statistically investigate events in the tail of heavy-tailed distributions. For this task, the peak-over-threshold approach is a common model, which crucially depends on the selection of a high threshold above which observations can be used for statistical inference. To improve the utility of threshold selection procedures, we propose two new methods and evaluate their performance theoretically and numerically in comparison to other approaches.
Keywords: Bayesian estimation; Extreme value analysis; Posterior contraction; Tuning parameter selection; Hill estimator