  This paper focuses on the influence of a misspecified covariance structure on
false discovery rate for the large scale multiple testing problem.
Specifically, we evaluate the influence on the marginal distribution of local
fdr statistics, which are used in many multiple testing procedures and related
to Bayesian posterior probabilities. Explicit forms of the marginal
distributions under both correctly specified and incorrectly specified models
are derived. The Kullback-Leibler divergence is used to quantify the influence
caused by a misspecification. Several numerical examples are provided to
illustrate the influence. A real spatio-temporal data on soil humidity is
discussed.
