Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behaviour of the empirical Bayes posteriors associated to
  maximum marginal likelihood estimator   We consider the asymptotic behaviour of the marginal maximum likelihood
empirical Bayes posterior distribution in general setting. First we
characterize the set where the maximum marginal likelihood estimator is located
with high probability. Then we provide oracle type of upper and lower bounds
for the contraction rates of the empirical Bayes posterior. We also show that
the hierarchical Bayes posterior achieves the same contraction rate as the
maximum marginal likelihood empirical Bayes posterior. We demonstrate the
applicability of our general results for various models and prior distributions
by deriving upper and lower bounds for the contraction rates of the
corresponding empirical and hierarchical Bayes posterior distributions.

22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga