Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantifying nuisance parameter effects via decompositions of asymptotic
  refinements for likelihood-based statistics   Accurate inference on a scalar interest parameter in the presence of a
nuisance parameter may be obtained using an adjusted version of the signed root
likelihood ratio statistic, in particular Barndorff-Nielsen's $R^*$ statistic.
The adjustment made by this statistic may be decomposed into a sum of two
terms, interpreted as correcting respectively for the possible effect of
nuisance parameters and the deviation from standard normality of the signed
root likelihood ratio statistic itself. We show that the adjustment terms are
determined to second-order in the sample size by their means. Explicit
expressions are obtained for the leading terms in asymptotic expansions of
these means. These are easily calculated, allowing a simple way of quantifying
and interpreting the respective effects of the two adjustments, in particular
of the effect of a high dimensional nuisance parameter. Illustrations are given
for a number of examples, which provide theoretical insight to the effect of
nuisance parameters on parametric inference. The analysis provides a
decomposition of the mean of the signed root statistic involving two terms: the
first has the property of taking the same value whether there are no nuisance
parameters or whether there is an orthogonal nuisance parameter, while the
second is zero when there are no nuisance parameters. Similar decompositions
are discussed for the Bartlett correction factor of the likelihood ratio
statistic, and for other asymptotically standard normal pivots.

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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph