Co-sufficient sampling refers to resampling the data conditional on a
sufficient statistic, a useful technique for statistical problems such as
goodness-of-fit tests, model selection, and confidence interval construction;
it is also a powerful tool to generate synthetic data which limits the
disclosure risk of sensitive data. However, sampling from such conditional
distributions is both technically and computationally challenging, and is
inapplicable in models without low-dimensional sufficient statistics.

We study an indirect inference approach to approximate co-sufficient
sampling, which only requires an efficient statistic rather than a sufficient
statistic. Given an efficient estimator, we prove that the expected KL
divergence goes to zero between the true conditional distribution and the
resulting approximate distribution. We also propose a one-step approximate
solution to the optimization problem that preserves the original estimator with
an error of $o_p(n^{-1/2})$, which suffices for asymptotic optimality. The
one-step method is easily implemented, highly computationally efficient, and
applicable to a wide variety of models, only requiring the ability to sample
from the model and compute an efficient statistic. We implement our methods via
simulations to tackle problems in synthetic data, hypothesis testing, and
differential privacy.

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Author Of this post: <a href="">Jordan Awan</a>, <a href="">Zhanrui Cai</a>

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