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Copulas have become very popular as a statistical model to representdependence structures between multiple variables in many applications. Given afinite number of constraints in advance, the minimum information copula is theclosest to the uniform copula when measured in Kullback-Leibler divergence. Forthese constraints, the expectation of moments such as Spearman's rho are mostlyconsidered in previous researches. These copulas are obtained as the optimalsolution to convex programming. On the other hand, other types of correlationhave not been studied previously in this context. In this paper, we presentMICK, a novel minimum information copula where Kendall's rank correlation isspecified. Although this copula is defined as the solution to non-convexoptimization problem, we show that the uniqueness of this copula is guaranteedwhen correlation is small enough. We also show that the family of checkerboardcopulas admits representation as non-orthogonal vector space. In doing so, weobserve local and global dependencies of MICK, thereby unifying results onminimum information copulas.

On the minimum information checkerboard copulas under fixed Kendall's rank correlation