Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The power of private likelihood-ratio tests for goodness-of-fit in
  frequency tables   Privacy-protecting data analysis investigates statistical methods under
privacy constraints. This is a rising challenge in modern statistics, as the
achievement of confidentiality guarantees, which typically occurs through
suitable perturbations of the data, may determine a loss in the statistical
utility of the data. In this paper, we consider privacy-protecting tests for
goodness-of-fit in frequency tables, this being arguably the most common form
of releasing data. Under the popular framework of
$(\varepsilon,\delta)$-differential privacy for perturbed data, we introduce a
private likelihood-ratio (LR) test for goodness-of-fit and we study its large
sample properties, showing the importance of taking the perturbation into
account to avoid a loss in the statistical significance of the test. Our main
contribution provides a quantitative characterization of the trade-off between
confidentiality, measured via differential privacy parameters $\varepsilon$ and
$\delta$, and utility, measured via the power of the test. In particular, we
establish a precise Bahadur-Rao type large deviation expansion for the power of
the private LR test, which leads to: i) identify a critical quantity, as a
function of the sample size and $(\varepsilon,\delta)$, which determines a loss
in the power of the private LR test; ii) quantify the sample cost of
$(\varepsilon,\delta)$-differential privacy in the private LR test, namely the
additional sample size that is required to recover the power of the LR test in
the absence of perturbation. Such a result relies on a novel multidimensional
large deviation principle for sum of i.i.d. random vectors, which is of
independent interest. Our work presents the first rigorous treatment of
privacy-protecting LR tests for goodness-of-fit in frequency tables, making use
of the power of the test to quantify the trade-off between confidentiality and
utility.

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The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
3
The categories of this paper are: physics