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Warsaw 2009: Presentations and short courses

On the smoothness of intersections of marginal conditional independencies

Session: Marginal models for dependent data

Authors:

Tamás Rudas; Eötvös Loránd University, Hungary
Wicher Bergsma; London School of Economics, United Kingdom
Renáta Németh; Eötvös Loránd University, Hungary

Abstract:

Statistical models are often defined by superimposing several simpler restrictions. The resulting models are intersections and one often hopes to derive the properties of the more complex model from that of the simpler ones. In a categorical data setting, smoothness of the resulting model is of fundamental importance. If holds, it implies standard asymptotic behavior when testing using chi-squared related statistics, but is also needed in the interpretation of parameters. The talk will present a general combinatorial condition for intersections of marginal independencies to be smooth. The usefulness of the condition will be illustrated by showing that it holds in problems related to repeated measurements, Markov chains and in certain block recursive models associated with chain graphs.