Testing goodness-of-fit and conditional independence with approximate co-sufficient sampling
使用近似共充分抽样检验拟合优度与条件独立性AI 解读 ↓
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使用近似共充分抽样检验拟合优度与条件独立性
- 研究问题
- 当复合原假设缺少紧凑充分统计量时，如何保留检验统计量选择的灵活性，同时控制拟合优度检验的一类错误？
- 方法与思路
- 作者用近似充分性推广共充分条件重抽样，将其扩展到具有渐近有效估计量的参数模型，并量化有限样本错误膨胀。
- 材料陈述的贡献
- 摘要称在标准最大似然渐近条件下，任意选定检验统计量对应的一类错误膨胀趋于消失，并通过理论与模拟研究功效。
- 阅读关注点
- 核对近似充分性的构造、条件重抽样如何实现、有限样本误差界，以及条件独立性检验所需的模型与估计条件。
- 阅读边界
- 仅据 OpenAlex 索引摘要，版本未注明；渐近错误膨胀消失不等于有限样本精确有效，条件独立性应用细节也未展开。
原文摘要
Goodness-of-fit (GoF) testing is ubiquitous in statistics, with direct ties to model selection, confidence interval construction, conditional independence testing, and multiple testing, just to name a few applications. While testing the GoF of a simple (point) null hypothesis provides an analyst great flexibility in the choice of test statistic while still ensuring validity, most GoF tests for composite null hypotheses are far more constrained, as the test statistic must have a tractable distribution over the entire null model space. A notable exception is co-sufficient sampling (CSS): resampling the data conditional on a sufficient statistic for the null model guarantees valid GoF testing using any test statistic the analyst chooses. But CSS testing requires the null model to have a compact (in an information-theoretic sense) sufficient statistic, which only holds for a very limited class of models; even for a null model as simple as logistic regression, CSS testing is powerless. In this paper, we leverage the concept of approximate sufficiency to generalize CSS testing to essentially any parametric model with an asymptotically efficient estimator; we call our extension “approximate CSS” (aCSS) testing. We quantify the finite-sample Type I error inflation of aCSS testing and show that it is vanishing under standard maximum likelihood asymptotics, for any choice of test statistic. We apply our proposed procedure both theoretically and in simulation to a number of models of interest to demonstrate its finite-sample Type I error and power.