PhD defence J.A. (Jochem) Oorschot

Dissertation in short:

A thesis on extremes in statistics and econometrics. Extreme value statistics is concerned with estimating probabilities of rare events. As an example, think of the probability of a large flood. In contrast with most traditional statistics, extreme value statistics does not use all available data but only the most extreme observations in the dataset. In the example of floods one could use the highest 1% water levels that have been recorded in the past 100 years to estimate the probability of a large future flood for example. Per definition the number of useful observations in extreme value statistics are scarcer than in traditional statistics. For that reason it is especially important to utilize the observations that you do have as efficiently as possible. In this thesis I developed new estimation methods to achieve this, so-called extreme U-statistics and the all block maxima (ABM) method. These methods are able to give better estimates of rare event probabilities than existing methods in some cases. Besides improving estimation methods I have considered the effect of extremes in the frequently used econometric OLS regression model. If the dependent variable has a tendency to take on very extreme values, then there is a possibility that the OLS estimates you obtain for the parameters of the independent variables deviate a lot from their theoretical values. Practitioners of OLS techniques ought to be aware of this fact.