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Some approximations of \(n\)-copulas. (English) Zbl 1197.62050

Summary: We consider several approximations to \(n\)-copulas: the checkmin, checkerboard, Bernstein, and shuffle of min approximations. The checkerboard, Bernstein, and shuffle of min approximations have been studied in the \(n = 2\) case. We investigate these constructions in arbitrary finite dimensions and consider some of the ways in which they converge or fail to converge to the original copula.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62E17 Approximations to statistical distributions (nonasymptotic)
62E20 Asymptotic distribution theory in statistics
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