Weak limits for exploratory plots in the analysis of extremes

Exploratory data analysis is often used to test the goodness-of-fit of sample observations to specific target distributions. A few such graphical tools have been extensively used to detect subexponential or heavy-tailed behavior in observed data. In this paper we discuss asymptotic limit behavior of...

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Bibliographic Details
Published in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2013-02, Vol.19 (1), p.308-343
Main Authors: DAS, BIKRAMJIT, GHOSH, SOUVIK
Format: Article
Language:English
Subjects:
asymptotic theory
Bridges
confidence bounds
Contour lines
Datasets
extreme values
Mathematical functions
ME plot
Null hypothesis
QQ plot
random set
Random variables
regular variation
Simulations
Statistics
Topological theorems
Topology
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Summary:Exploratory data analysis is often used to test the goodness-of-fit of sample observations to specific target distributions. A few such graphical tools have been extensively used to detect subexponential or heavy-tailed behavior in observed data. In this paper we discuss asymptotic limit behavior of two such plotting tools: the quantile—quantile plot and the mean excess plot. The weak consistency of these plots to fixed limit sets in an appropriate topology of ℝ 2 has been shown in Das and Resnick (Stoch. Models 24 (2008) 103—132) and Ghosh and Resnick (Stochastic Process. Appl. 120 (2010) 1492—1517). In this paper we find asymptotic distributional limits for these plots when the underlying distributions have regularly varying right-tails. As an application we construct confidence bounds around the plots which enable us to statistically test whether the underlying distribution is heavy-tailed or not.
ISSN:1350-7265
DOI:10.3150/11-BEJ401