Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Impossibility Results for Inference With Cluster Dependence with
  Large Clusters   There have appeared in the literature various approaches of inference for
models with cluster dependence with few clusters, where the dependence
structure within each cluster is unknown. These approaches are all different
from the "standard" approach of asymptotic inference based on an asymptotically
pivotal test. One may wonder whether it is possible to develop a standard
asymptotic inference in this situation. To answer this question, we focus on a
Gaussian experiment, and present a necessary and sufficient condition for the
cluster structure that the long run variance is consistently estimable. Our
result implies that when there is at least one large cluster, the long run
variance is not consistently estimable, and hence, the standard approach of
inference based on an asymptotically pivotal test is not possible. This
impossibility result extends to other models that contain a Gaussian experiment
as a special case. As a second focus, we investigate the consistent
discrimination of the common mean from a sample with cluster dependence. We
show that when the observations consist of large clusters, it is necessary for
the consistent discrimination of the mean that the sample has at least two
large clusters. This means that if one does not know the dependence structure
at all, it is not possible to consistently discriminate the mean.

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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin