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A note on the IPF algorithm when the marginal problem is unsolvable. (English) Zbl 1245.62070
Summary: We analyze the asymptotic behavior of the IPF algorithm for the problem of finding a \(2\times 2\times 2\) contingency table whose pair marginals are all equal to a specified \(2\times 2\) table, depending on a parameter. When this parameter lies below a certain threshold the marginal problem has no solution. We show that in this case the IPF has a “period three limit cycle” attracting all positive initial tables, and a bifurcation occurs when the parameter crosses the threshold.

62H17 Contingency tables
65C60 Computational problems in statistics (MSC2010)
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