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Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete variables.
A stochastic approximation method
Robbins, H. and Monro, S. (1951) · 1951
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Sklar, A. (1959) · 1959
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Ware, J. E., Snow, K. K., Kolinski, M., and Gandeck, B. (1993) · 1993
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Roberts, G. O., Gelman, A., and Gilks, W. R. (1997) · 1997
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