Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Classical and Bayesian Asymptotics in Stochastic Differential
  Equations with Random Effects having Mixture Normal Distributions   Delattre et al. (2013) considered a system of stochastic differential
equations (SDEs) in a random effects setup. Under the independent and identical
(iid) situation, and assuming normal distribution of the random effects, they
established weak consistency of the maximum likelihood estimators (M LEs) of
the population parameters of the random effects.
  In this article, respecting the increasing importance and versatility of
normal mixtures and their ability to approximate any standard distribution, we
consider the random effects having mixture of normal distributions and prove
asymptotic results associated with the MLEs in both independent and identical
(iid) and independent but not identical (non-iid) situations. Besides, we
consider iid and non-iid setups under the Bayesian paradigm and establish
posterior consistency and asymptotic normality of the posterior distribution of
the population parameters, even when the number of mixture components is
unknown and treated as a random variable.
  Although ours is an independent work, we later noted that Delattre et al.
(2016) also assumed the SDE setup with normal mixture distribution of the
random effect parameters but considered only the iid case and proved only weak
consistency of the M LE under an extra, strong assumption as opposed to strong
consistency that we are able to prove without the extra assumption.
Furthermore, they did not deal with asymptotic normality of M LE or the
Bayesian asymptotics counterpart which we investigate in details.
  Ample simulation experiments and application to a real, stock market data set
reveal the importance and usefulness of our methods even for small samples.

24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an