Exactly and almost compatible joint distributions for high-dimensional discrete conditional distributions. (English) Zbl 1362.62119
Summary: A conditional model is a set of conditional distributions, which may be compatible or incompatible, depending on whether or not there exists a joint distribution whose conditionals match the given conditionals. In this paper, we propose a new mathematical tool called a “structural ratio matrix” (SRM) to develop a unified compatibility approach for discrete conditional models. With this approach, we can find all joint pdfs after confirming that the given model is compatible. In practice, it is most likely that the conditional models we encounter are incompatible. Therefore, it is important to investigate approximated joint distributions for them. We use the concept of SRM again to construct an almost compatible joint distribution, with consistency property, to represent the given incompatible conditional model.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62E17 | Approximations to statistical distributions (nonasymptotic) |
Keywords:
almost compatible joint distribution; compatibility; full conditional distributions; incompatibility; irreducible block diagonal matrix; rank one positive extension matrix; structural ratio matrixReferences:
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