论文标题
关于分裂似然比测试的分裂比的选择
On the choice of the splitting ratio for the split likelihood ratio test
论文作者
论文摘要
最近引入的通用推理框架为构建有限样本中有效的假设检验和置信区域提供了一种新的方法，并且不依赖于基础统计模型上的任何特定的规律性假设。该方法的核心是一个分裂的似然比统计量，该统计量是在数据拆分下形成的，并将其与巧妙选择的通用临界值进行了比较。由于这种临界价值可能非常保守，因此通过仔细选择比率来减轻电力的潜在损失是有趣的。在此问题的促进下，我们研究了局部替代方案下的分裂似然比测试，并介绍了由此产生的非中央分裂卡方分布。我们研究了这一新的分布类别的属性，并使用它来数字检查并提出了数据拆分率的最佳选择，以测试不同维度的复合假设。
The recently introduced framework of universal inference provides a new approach to constructing hypothesis tests and confidence regions that are valid in finite samples and do not rely on any specific regularity assumptions on the underlying statistical model. At the core of the methodology is a split likelihood ratio statistic, which is formed under data splitting and compared to a cleverly selected universal critical value. As this critical value can be very conservative, it is interesting to mitigate the potential loss of power by careful choice of the ratio according to which data are split. Motivated by this problem, we study the split likelihood ratio test under local alternatives and introduce the resulting class of noncentral split chi-square distributions. We investigate the properties of this new class of distributions and use it to numerically examine and propose an optimal choice of the data splitting ratio for tests of composite hypotheses of different dimensions.
