Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Smoothed P-Value Test When There is a Nuisance Parameter under the
  Alternative   We present a new test when there is a nuisance parameter under the
alternative hypothesis. The test exploits the p-value occupation time [PVOT],
the measure of the subset of a nuisance parameter on which a p-value test
rejects the null hypothesis. Key contributions are: (i) An asymptotic critical
value upper bound for our test is the significance level, making inference
easy. Conversely, test statistic functionals need a bootstrap or simulation
step which can still lead to size and power distortions, and bootstrapped or
simulated critical values are not asymptotically valid under weak or
non-identification. (ii) We only require the test statistic to have a known or
bootstrappable limit distribution, hence we do not require root(n)-Gaussian
asymptotics, and weak or non-identification is allowed. Finally, (iii) a test
based on the sup-p-value may be conservative and in some cases have nearly
trivial power, while the PVOT naturally controls for this by smoothing over the
nuisance parameter space. We give examples and related controlled experiments
concerning PVOT tests of: omitted nonlinearity with and without the possibility
of weakly identified model parameters; GARCH effects. Across cases, the PVOT
test variously matches, dominates or strongly dominates standard tests based on
the supremum p-value, or supremum or average test statistic (with wild
bootstrapped p-value)

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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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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: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat