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A practical method for analysing heavy tailed data
Author(s) -
Peng Liang
Publication year - 2009
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.10018
Subject(s) - estimator , quantile , statistics , interval estimation , point estimation , index (typography) , estimation , heavy tailed distribution , statistical inference , fraction (chemistry) , mathematics , inference , sample size determination , econometrics , confidence interval , computer science , probability distribution , artificial intelligence , economics , chemistry , management , organic chemistry , world wide web
An important practical issue of applying heavy tailed distributions is how to choose the sample fraction or threshold, since only a fraction of upper order statistics can be employed in the inference. Recently, Guillou & Hall (2001; Journal of Royal Statistical Society B , 63, 293–305) proposed a simple way to choose the threshold in estimating a tail index. In this article, the author first gives an intuitive explanation of the approach in Guillou & Hall (2001; it Journal of Royal Statistical Society B , 63, 293–305) and then proposes an alternative method, which can be extended to other settings like extreme value index estimation and tail dependence function estimation. Further the author proposes to combine this method for selecting a threshold with a bias reduction estimator to improve the performance of the tail index estimation, interval estimation of a tail index, and high quantile estimation. Simulation studies on both point estimation and interval estimation for a tail index show that both selection procedures are comparable and bias reduction estimation with the threshold selected by either method is preferred. The Canadian Journal of Statistics © 2009 Statistical Society of Canada