The saddle-point method and its application to the hill estimator

Buitendag, Sven (2016-12)

Thesis (MCom)--Stellenbosch University, 2016.

Thesis

ENGLISH SUMMARY : The saddle-point approximation is a highly accurate approximation of the distribution of a random variable. It was originally derived as an approximation in situations where a parameter takes on large values. However, due to its high accuracy and good behaviour in a variety of applications not involving such a parameter, it has been generalized and applied to the distribution of any random variable with a well-behaved cumulant generating function. In this thesis the theory underlying the saddle-point approximation will be discussed and illustrated with an application to approximate the distribution of the Hill estimator in extreme value theory.

AFRIKAANSE OPSOMMING : Die saalpunt-benadering is 'n hoogs noukeurige benadering van die verdeling van 'n stochastiese veranderlike. Dit is oorspronklik afgelei as 'n benadering in gevalle waar 'n parameter groot waardes aanneem. Nietemin, na aanleiding van sy hoogs akkurate aard en goeie gedrag in 'n verskeidenheid van toepassings wat nie betrekking het op so 'n parameter nie, is dit veralgemeen en toegepas op die verdeling van enige stochastiese veranderlike met 'n kumulantvoortbringende funksie wat goeie gedrag toon. In hierdie tesis sal die teorie onderliggend aan die saalpunt-benadering bespreek en gellustreer word met 'n toepassing om die verdeling van die Hill-beramer te benader.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/100057
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