Unbiasedness of the Likelihood Ratio Test for Lattice Conditional Independence Models

The lattice conditional independence (LCI) model N() is defined to be the set of all normal distributions N(0, [Sigma]) on I such that for every pair L, M [set membership, variant] , xL and xM are conditionally independent given xL [intersection] M. Here is a ring of subsets (hence a distributive lattice) of the finite index set I such that [empty set][combining character] I [set membership, variant] , while for K [set membership, variant] , xK is the coordinate projection of x [set membership, variant] I onto K. Andersson and Perlman in the preceding paper derived the likelihood ratio (LR) statistic [lambda] for testing one LCI model against another, i.e., for testing N() vs N() based on a random sample from N(0, [Sigma]), where is a subring of . In the present paper the strict unbiasedness of the LR test is established, and related results regarding the distribution of the maximum likelihood estimator of [Sigma] under the LCI model N() are presented.