Title: Exact model comparisons in the plausibility framework Show Chinese title

Title: 合理性框架下的精确模型比较

Abstract: 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 $\alpha$ 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. Show Chinese abstract

Abstract: 似然性是对参数模型的精确检验的形式化，并推广了诸如Fisher精确检验之类的程序。 由此产生的检验基于概率密度函数的累积概率，并评估与参数族的一致性，同时对于有限样本大小提供精确的 $\alpha$ 水平控制。 在这种方法中，模型比较效率较低。 我们通过引入加权来推广似然性，这允许执行模型比较。 我们证明了一种加权方案渐近等价于似然比检验（LRT），并且在零假设下具有有限样本保证的检验水平，这与LRT不同。 我们在模拟数据集中验证理论属性，这些数据集模仿了我们的数据分析数据集。 我们将该方法应用于视网膜母细胞瘤数据集，并展示了亲本起源效应。 加权似然性在高维数据分析中也有应用，可以推导出惩罚回归模型的P值。 我们通过模拟研究证明了其相对于数据分割程序的优越性能。 我们将加权似然性应用于高维基因表达、病例对照前列腺癌数据集。 我们通过将加权似然性与目标学习、自助法和稀疏选择联系起来，讨论了该方法的灵活性。