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February 2013 Weak limits for exploratory plots in the analysis of extremes
Bikramjit Das, Souvik Ghosh
Bernoulli 19(1): 308-343 (February 2013). DOI: 10.3150/11-BEJ401

Abstract

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 $\mathbb{R}^{2}$ 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.

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Bikramjit Das. Souvik Ghosh. "Weak limits for exploratory plots in the analysis of extremes." Bernoulli 19 (1) 308 - 343, February 2013. https://doi.org/10.3150/11-BEJ401

Information

Published: February 2013
First available in Project Euclid: 18 January 2013

zbMATH: 1288.62076
MathSciNet: MR3019497
Digital Object Identifier: 10.3150/11-BEJ401

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

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Vol.19 • No. 1 • February 2013
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