Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Maximum Likelihood Estimators and their applications to
  stratified sampling and post-stratification with many unobserved strata   Consider the problem of estimating a weighted average of the means of $n$
strata, based on a random sample with realized $K_i$ observations from stratum
$i, \; i=1,...,n$.
  This task is non-trivial in cases where for a significant portion of the
strata the corresponding $K_i=0$. Such a situation may happen in
post-stratification, when it is desired to have a very fine sftratification. A
fine stratification could be desired in order that assumptions, or,
approximations, like Missing At Random conditional on strata, will be
appealing. A fine stratification could also be desired in observational
studies, when it is desired to estimate average treatment effect, by averaging
the effects in small and homogenous strata.
  Our approach is based on applying Generalized Maximum Likelihood Estimators
(GMLE), and ideas that are related to Non-Parametric Empirical Bayes, in order
to estimate the means of strata $i$ with corresponding $K_i=0$. There are no
assumptions about a relation between the means of the unobserved strata (i.e.,
with $K_i=0$) and those of the observed strata.
  The performance of our approach is demonstrated both in simulations and on a
real data set. Some consistency and asymptotic results are also presented. In
addition, related basic results about GMLE estimation of the mean of mixtures
of exponential families are provided.

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The categories of this paper are: math-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-th