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<p>Classifying a data set as asymptotically dependent (ADep) or asymptotically independent (AInd) is a necessary early choice in the modeling of multivariate extremes. These two dependence regimes are defined asymptotically which complicates inference as practitioners have finite samples. We perform a series of experiments to determine whether a finite sample has enough information for a neural network to reliably distinguish between these regimes in the bivariate case. Along the way we develop a new classification tool for practitioners which we call nnadic as it is a <b>N</b>eural <b>N</b>etwork for <b>A</b>symptotic <b>D</b>ependence/<b>I</b>ndependence <b>C</b>lassification. This tool accurately classifies over 95% of test datasets and is robust to a wide range of sample sizes. The datasets which we are unable to correctly classify tend to either be nearly exactly independent or exhibit near perfect dependence, which are boundary cases for both the ADep and AInd models used for training. These experiments highlight that ADep and AInd models do not so much differ in the strength of tail dependence they can capture (as both regimes can range from independence to complete dependence), but they instead differ in whether the dependence completely decays in the limit, irrespective of the path of that decay.</p>

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Neural classification of asymptotic (in)dependence

  • 期刊论文

  • 发表日期：

    2025年9月10日

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  • Troy P. Wixson,
  • Daniel Cooley

摘要

Classifying a data set as asymptotically dependent (ADep) or asymptotically independent (AInd) is a necessary early choice in the modeling of multivariate extremes. These two dependence regimes are defined asymptotically which complicates inference as practitioners have finite samples. We perform a series of experiments to determine whether a finite sample has enough information for a neural network to reliably distinguish between these regimes in the bivariate case. Along the way we develop a new classification tool for practitioners which we call nnadic as it is a Neural Network for Asymptotic Dependence/Independence Classification. This tool accurately classifies over 95% of test datasets and is robust to a wide range of sample sizes. The datasets which we are unable to correctly classify tend to either be nearly exactly independent or exhibit near perfect dependence, which are boundary cases for both the ADep and AInd models used for training. These experiments highlight that ADep and AInd models do not so much differ in the strength of tail dependence they can capture (as both regimes can range from independence to complete dependence), but they instead differ in whether the dependence completely decays in the limit, irrespective of the path of that decay.