Space-efficient estimation of empirical tail dependence coefficients for bivariate data streams

02/10/2019

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by   Alastair Gregory, et al.

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This article provides an extension to recent work on the development of a space-efficient summary for bivariate empirical copula approximations in a streaming data regime. The extension proposed here considers the case when one would like to accurately approximate the bivariate empirical copula in the tails of each marginal distribution; therefore modelling the tail dependence between the two variables observed in the data stream. Copulas evaluated at these marginal tails can be used to estimate the tail dependence coefficient. The modifications to the bivariate copula approximation, presented in this paper, allow the error of an approximation to the tail dependence coefficient to remain invariant of the length of the data stream. Theoretical and numerical evidence is provided within this article to support this.