Factorization of the Cumulative Distribution Function in Case of Conditional Independence. (REVISED, November 1999).
Sonderforschungsbereich 386, Discussion Paper 161
A decomposition of complex estimation problems is often obtained by using factorization formulas for the underlying likelihood or density function. This is, for instance, the case in so-called decomposable graphical models where under the restrictions of conditional independences induced by the graph the estimation in the original model may be decomposed into estimation problems corresponding to subgraphs. Such a decomposition is based on the property of conditional independence which can be read off the graph and on the factorization of the assumed underlying density function. In this paper analogous factorization formulas for the cumulative distribution function are introduced which can be useful in situations where the density is not tractable.