Unbiasedness of the Likelihood Ratio Test for Lattice Conditional Independence Models

The lattice conditional independence (LCI) model N( K ) is defined to be the set of all normal distributions N(0, Σ) on R I such that for every pair L, M ∈ K , x L and x M are conditionally independent given x L ∩ M . Here K is a ring of subsets (hence a distributive lattice) of the finite index set...

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Bibliographic Details
Published in:Journal of multivariate analysis 1995-04, Vol.53 (1), p.1-17
Main Authors: Andersson, S.A., Perlman, M.D.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Multivariate analysis
Probability and statistics
Sciences and techniques of general use
Statistics
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Summary:The lattice conditional independence (LCI) model N( K ) is defined to be the set of all normal distributions N(0, Σ) on R I such that for every pair L, M ∈ K , x L and x M are conditionally independent given x L ∩ M . Here K is a ring of subsets (hence a distributive lattice) of the finite index set I such that ∅ I ∈ K , while for K ∈ K , x K is the coordinate projection of x ∈ R I onto R K . Andersson and Perlman in the preceding paper derived the likelihood ratio (LR) statistic λ for testing one LCI model against another, i.e., for testing N( K ) vs N( M ) based on a random sample from N(0, Σ), where M is a subring of K . 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 Σ under the LCI model N( K ) are presented.
ISSN:0047-259X
1095-7243
DOI:10.1006/jmva.1995.1021