论文标题
更强大的t检验
A More Robust t-Test
论文作者
论文摘要
通过GMM估计的标量参数的标准推论量相当于将t检验应用于特定的观测值。如果观察值的数量不是很大，则适度重的尾巴会导致t检验的行为不佳。这是聚类下的一个特殊问题，因为当时观察值对应于簇的数量，而聚类尺寸的异质性会引起沉重的尾巴。本文结合了最小和最大的观测值的极端价值理论，以及其余观测值平均值的正常近似值，以构建t检验更强大的替代方案。与现有方法相比，在小样本中发现新测试可以更成功地控制尺寸。分析结果对平均问题的规范推断表明，在超过两个以上但少于三个时刻的情况下，新测试对完整的样本t检验提供了完善，而自举t检验则没有。
Standard inference about a scalar parameter estimated via GMM amounts to applying a t-test to a particular set of observations. If the number of observations is not very large, then moderately heavy tails can lead to poor behavior of the t-test. This is a particular problem under clustering, since the number of observations then corresponds to the number of clusters, and heterogeneity in cluster sizes induces a form of heavy tails. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the average of the remaining observations to construct a more robust alternative to the t-test. The new test is found to control size much more successfully in small samples compared to existing methods. Analytical results in the canonical inference for the mean problem demonstrate that the new test provides a refinement over the full sample t-test under more than two but less than three moments, while the bootstrapped t-test does not.
