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Exact model comparisons in the plausibility framework
Journal of Statistical Planning and Inference ( IF 0.9 ) Pub Date : 2021-09-07 , DOI: 10.1016/j.jspi.2021.07.013
Stefan Böhringer 1 , Dietmar Lohmann 2
Affiliation  

Plausibility is a formalization of exact tests for parametric models and generalizes procedures such as Fisher’s exact test. The resulting tests are based on cumulative probabilities of the probability density function and evaluate consistency with a parametric family while providing exact control of the α level for finite sample size. Model comparisons are inefficient in this approach. We generalize plausibility by incorporating weighing which allows to perform model comparisons. We show that one weighing scheme is asymptotically equivalent to the likelihood ratio test (LRT) and has finite sample guarantees for the test size under the null hypothesis unlike the LRT. We confirm theoretical properties in simulations that mimic the data set of our data application. We apply the method to a retinoblastoma data set and demonstrate a parent-of-origin effect.

Weighted plausibility also has applications in high-dimensional data analysis and P-values for penalized regression models can be derived. We demonstrate superior performance as compared to a data-splitting procedure in a simulation study. We apply weighted plausibility to a high-dimensional gene expression, case-control prostate cancer data set.

We discuss the flexibility of the approach by relating weighted plausibility to targeted learning, the bootstrap, and sparsity selection.



中文翻译:

合理性框架中的精确模型比较

合理性是参数模型精确检验的形式化,并概括了诸如 Fisher 精确检验之类的程序。结果测试基于概率密度函数的累积概率,并评估与参数族的一致性,同时提供对α有限样本量的水平。在这种方法中模型比较是低效的。我们通过结合允许执行模型比较的权重来概括合理性。我们表明,一种加权方案渐近等效于似然比检验 (LRT),并且与 LRT 不同,在零假设下对检验规模具有有限样本保证。我们在模拟我们的数据应用程序的数据集的模拟中确认了理论属性。我们将该方法应用于视网膜母细胞瘤数据集,并证明了亲本效应。

加权似真度在高维数据分析和 可以导出惩罚回归模型的值。与模拟研究中的数据拆分程序相比,我们展示了优越的性能。我们将加权合理性应用于高维基因表达、病例对照前列腺癌数据集。

我们通过将加权合理性与目标学习、引导程序和稀疏选择相关联来讨论该方法的灵活性。

更新日期:2021-09-20
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