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The Annals of Applied Statistics 2008, Vol. 2, No. 3, 10781102
 

Summary: The Annals of Applied Statistics
2008, Vol. 2, No. 3, 1078­1102
DOI: 10.1214/08-AOAS173
© Institute of Mathematical Statistics, 2008
ANALYSIS OF COMPARATIVE DATA WITH
HIERARCHICAL AUTOCORRELATION
BY CÉCILE ANÉ
University of Wisconsin--Madison
The asymptotic behavior of estimates and information criteria in linear
models are studied in the context of hierarchically correlated sampling units.
The work is motivated by biological data collected on species where auto-
correlation is based on the species' genealogical tree. Hierarchical autocor-
relation is also found in many other kinds of data, such as from microarray
experiments or human languages. Similar correlation also arises in ANOVA
models with nested effects. I show that the best linear unbiased estimators are
almost surely convergent but may not be consistent for some parameters such
as the intercept and lineage effects, in the context of Brownian motion evolu-
tion on the genealogical tree. For the purpose of model selection I show that
the usual BIC does not provide an appropriate approximation to the posterior
probability of a model. To correct for this, an effective sample size is intro-

  

Source: Ané, Cécile - Departments of Botany & Statistics, University of Wisconsin at Madison

 

Collections: Biology and Medicine; Mathematics