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Space‐efficient estimation of empirical tail dependence coefficients for bivariate data streams
Author(s) -
Gregory Alastair,
Jana Kaushik
Publication year - 2020
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11439
Subject(s) - bivariate analysis , copula (linguistics) , marginal distribution , mathematics , bivariate data , parameter space , invariant (physics) , tail dependence , statistics , econometrics , statistical physics , multivariate statistics , random variable , physics , mathematical physics
This article proposes a space‐efficient approximation to empirical tail dependence coefficients of an indefinite bivariate stream of data. The approximation, which has stream‐length invariant error bounds, utilizes recent work on the development of a summary for bivariate empirical copula functions. The work in this paper accurately approximates a bivariate empirical copula in the tails of each marginal distribution, therefore modeling 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 coefficients. Modifications to the space‐efficient bivariate copula approximation, presented in this paper, allow the error of approximations to the tail dependence coefficients to remain stream‐length invariant. Theoretical and numerical evidence of this, including a case‐study using the Los Alamos National Laboratory netflow data‐set, is provided within this article.