Lattice Models for Conditional Independence in a Multivariate Normal Distribution

The lattice conditional independence model N(X) is defined to be the set of all normal distributions on WRI such that for every pair L, M E X, XL and XM are conditionally independent given XL n M. Here X is a ring of subsets of the finite index set I and, for K E X, XK is the coordinate projection of x E HII onto RK* Statistical properties of N(Y) may be studied, for example, maximum likelihood inference, invariance and the problem of testing Ho: N(X) vs. H: N(.1) when ,W is a subring of X. The set J(X) of join-irreducible elements of XY plays a central role in the analysis of N(X). This class of statistical models occurs in the analysis of nonnested multivariate missing data patterns and nonnested dependent linear regression models.

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