Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Opportunistic Detection Rules: Finite and Asymptotic Analysis   Opportunistic detection rules (ODRs) are variants of fixed-sample-size
detection rules in which the statistician is allowed to make an early decision
on the alternative hypothesis opportunistically based on the sequentially
observed samples. From a sequential decision perspective, ODRs are also
mixtures of one-sided and truncated sequential detection rules. Several results
regarding ODRs are established in this paper. In the finite regime, the maximum
sample size is modeled either as a fixed finite number, or a geometric random
variable with a fixed finite mean. For both cases, the corresponding Bayesian
formulations are investigated. The former case is a slight variation of the
well-known finite-length sequential hypothesis testing procedure in the
literature, whereas the latter case is new, for which the Bayesian optimal ODR
is shown to be a sequence of likelihood ratio threshold tests with two
different thresholds: a running threshold, which is determined by solving a
stationary state equation, is used when future samples are still available, and
a terminal threshold (simply the ratio between the priors scaled by costs) is
used when the statistician reaches the final sample and thus has to make a
decision immediately. In the asymptotic regime, the tradeoff among the
exponents of the (false alarm and miss) error probabilities and the normalized
expected stopping time under the alternative hypothesis is completely
characterized and proved to be tight, via an information-theoretic argument.
Within the tradeoff region, one noteworthy fact is that the performance of the
Stein-Chernoff Lemma is attainable by ODRs.

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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio