近似共充分采样与正则化
Approximate co-sufficient sampling with regularization
AI总结：
本文扩展了近似共充分采样方法，使其适用于约束和正则化最大似然估计，解决了复杂估计问题。
摘要：
在本文中，我们考虑参数模型的拟合优度（GoF）检验问题。该检验问题涉及一个复合原假设，由于模型参数的未知值。在某些特殊情况下，共充分采样（CSS）可以通过对充分统计量进行条件化来消除这些未知参数的影响——通常，最大似然估计（MLE）用于估计未知参数。然而，许多常见的参数设置并不允许这种方法，因为对充分统计量进行条件化会导致无效力的检验。最近的近似共充分采样（aCSS）框架（Barber和Janson，2022）提供了一种替代方法，用近似充分统计量（即MLE的噪声版本）替代充分性。这种方法在CSS无法应用的许多设置中恢复了效力，但只能在未受约束的MLE良好定义且行为良好的设置中应用，这隐含地假设了一个低维领域。在本文中，我们扩展了aCSS到约束和正则化最大似然估计的设置，使得更复杂的估计问题现在可以在这个aCSS框架内处理，包括混合高斯模型（由于退化，未受约束的MLE未良好定义）和高维高斯线性模型（其中MLE在正则化下表现良好，如ℓ1惩罚或形状约束）。
英文摘要：
In this work, we consider the problem of goodness-of-fit (GoF) testing for parametric models. This testing problem involves a composite null hypothesis, due to the unknown values of the model parameters. In some special cases, co-sufficient sampling (CSS) can remove the influence of these unknown parameters via conditioning on a sufficient statistic -- often, the maximum likelihood estimator (MLE) of the unknown parameters. However, many common parametric settings do not permit this approach, since conditioning on a sufficient statistic leads to a powerless test. The recent approximate co-sufficient sampling (aCSS) framework of Barber and Janson (2022) offers an alternative, replacing sufficiency with an approximately sufficient statistic (namely, a noisy version of the MLE). This approach recovers power in a range of settings where CSS cannot be applied, but can only be applied in settings where the unconstrained MLE is well-defined and well-behaved, which implicitly assumes a low-dimensional regime. In this work, we extend aCSS to the setting of constrained and penalized maximum likelihood estimation, so that more complex estimation problems can now be handled within the aCSS framework, including examples such as mixtures-of-Gaussians (where the unconstrained MLE is not well-defined due to degeneracy) and high-dimensional Gaussian linear models (where the MLE can perform well under regularization, such as an $\ell_1$ penalty or a shape constraint).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
