论文标题
TE测试：用于Behrens-Fisher问题的新的非反应t检验
Te Test: A New Non-asymptotic T-test for Behrens-Fisher Problems
论文作者
论文摘要
Behrens-Fisher问题是一个经典的统计问题。当尚不清楚的种群方差的平等时，使用两个独立样本测试两个正常人群的平等。 Linnik（1968）表明，基于完整的统计数据，此问题没有确切的固定级测试。但是，确实存在基于其他统计数据和近似解决方案的确切常规解决方案。 现有方法主要是渐近测试，通常在方差或样本量差异很大时表现不佳。在本文中，我们提出了一种新方法，以找到一个确切的t检验（TE）来解决这个经典的behrens-fisher问题。提供两种均值之间差异的置信区间。我们还使用详细的分析表明，TE测试达到了最大的自由度，并给出了薄弱的证明TE测试的置信区间期望值最短。进行了一些模拟，以显示我们新提出的方法与可用的常规方法（如Welch的测试，配对t检验等）相比的优势。我们还将将其与非常规的方法进行比较，例如两阶段测试。
The Behrens-Fisher Problem is a classical statistical problem. It is to test the equality of the means of two normal populations using two independent samples, when the equality of the population variances is unknown. Linnik (1968) has shown that this problem has no exact fixed-level tests based on the complete sufficient statistics. However, exact conventional solutions based on other statistics and approximate solutions based the complete sufficient statistics do exist. Existing methods are mainly asymptotic tests, and usually don't perform well when the variances or sample sizes differ a lot. In this paper, we propose a new method to find an exact t-test (Te) to solve this classical Behrens-Fisher Problem. Confidence intervals for the difference between two means are provided. We also use detailed analysis to show that Te test reaches the maximum of degree of freedom and to give a weak version of proof that Te test has the shortest confidence interval length expectation. Some simulations are performed to show the advantages of our new proposed method compared to available conventional methods like Welch's test, paired t-test and so on. We will also compare it to unconventional method, like two-stage test.
