A1192
Title: Statistical inference with the modified Greenwood statistic for univariate and multivariate heavy-tailed models
Authors: Marek Arendarczyk - University of Wroclaw (Poland)
Tomasz Kozubowski - University of Nevada Reno (United States)
Anna Panorska - University of Nevada (United States)
Katarzyna Skowronek - Wroclaw University of Science and Technology (Poland)
Agnieszka Wylomanska - Wroclaw University of Science and Technology (Poland)
Marek Arendarczyk - University of Wroclaw (Poland) [presenting]
Abstract: The Greenwood statistic and its modifications play an important role in modern statistical methodology for extremes, heavy-tailed distributions, and non-Gaussian models. Originally introduced for testing exponentiality, the statistic has since been developed into a versatile tool with applications in extreme value analysis and the study of clustering and heterogeneity. Recent results demonstrate stochastic ordering of the Greenwood statistic with respect to the tail index, which makes it suitable for building tests and confidence intervals in families of distributions relevant for extreme value theory. Further developments adapt the modified Greenwood statistic to symmetric alpha-stable and Student's t families of distributions. In addition, a multivariate generalization has been proposed, extending the use of the Greenwood framework to vector-valued samples, including the sub-Gaussian case, multivariate Pareto, and multivariate Student's t families of distributions. Consequently, the modified Greenwood statistic enables effective testing of multivariate Gaussianity, identification of infinite variance, and discrimination between heavy- and light-tailed multivariate models. The mathematical framework is discussed in stochastic ordering results, simulation studies, and real data applications, emphasizing the modified Greenwood statistic as an important and efficient tool in statistical inference.
