A0836
Title: Generalized Taylor's law for dependent and heterogeneous heavy-tailed data
Authors: Pok Him Cheng - Columbia University in the City of New York (United States) [presenting]
Brian Ling - Queens University ()
Phillip Yam - Chinese University of Hong Kong (Hong Kong)
Joel Cohen - The Rockefeller University (United States)
Abstract: Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is a widely observed empirical pattern across disciplines such as ecology, physics, finance, and epidemiology. It states that the variance of a sample is proportional to the power of its mean. Taylor's law is studied in the context of heavy-tailed distributions with infinite mean and variance. The probabilistic limit is established, and the associated convergence rates are analyzed. Results extend the existing literature by relaxing the i.i.d. assumption, allowing for weak dependence among the random variables. This generalization enables findings to apply to dependent data settings, including time series and network-structured data. The theoretical developments are supported by extensive simulation studies, and practical relevance is illustrated through an application to real-world network data.
