|
Abstract:
|
Co-sufficient sampling refers to resampling the data conditional on a sufficient statistic, a technique applied to problems such as goodness-of-fit tests, model selection, and confidence interval construction; it is also a powerful tool to generate privacy-preserving synthetic data. However, co-sufficient sampling is both technically and computationally challenging, and is inapplicable in models without low-dimensional sufficient statistics.
We extend an indirect inference approach to CSS to a much broader setting, only requiring an efficient statistic. 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 $o_p(n^{-1/2})$. Our 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.
|
