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Abstract: The asymptotic behavior of estimates and information criteria in linearmodels are studied in the context of hierarchically correlated sampling units.The work is motivated by biological data collected on species whereautocorrelation is based on the species- genealogical tree. Hierarchicalautocorrelation is also found in many other kinds of data, such as frommicroarray experiments or human languages. Similar correlation also arises inANOVA models with nested effects. I show that the best linear unbiasedestimators are almost surely convergent but may not be consistent for someparameters such as the intercept and lineage effects, in the context ofBrownian motion evolution on the genealogical tree. For the purpose of modelselection I show that the usual BIC does not provide an appropriateapproximation to the posterior probability of a model. To correct for this, aneffective sample size is introduced for parameters that are inconsistentlyestimated. For biological studies, this work implies that tree-aware samplingdesign is desirable; adding more sampling units may not help ancestralreconstruction and only strong lineage effects may be detected with high power.

Author: Cécile Ané


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