论文标题
多元位置的贝叶斯非参数测试
Bayesian nonparametric tests for multivariate locations
论文作者
论文摘要
在本文中，我们提出了针对单样本和两样本多元位置问题的新型贝叶斯非参数测试。我们先前使用Dirichlet过程对基础分布进行建模，并根据分布的空间中位功能基于后验可信区域制定测试程序。对于一个样本问题，如果可信集包含零值，我们将无法拒绝零假设。对于两个样本问题，我们为两个样本的空间中位数的差异构成可靠的集合，如果可靠集合零，我们将无法拒绝平等的零假设。我们在收缩替代方案下得出了测试的局部渐近力，并提出了一项模拟研究，以将测试程序的有限样本性能与现有参数和非参数测试进行比较。
In this paper, we propose novel, fully Bayesian non-parametric tests for one-sample and two-sample multivariate location problems. We model the underlying distribution using a Dirichlet process prior, and develop a testing procedure based on the posterior credible region for the spatial median functional of the distribution. For the one-sample problem, we fail to reject the null hypothesis if the credible set contains the null value. For the two-sample problem, we form a credible set for the difference of the spatial medians of the two samples and we fail to reject the null hypothesis of equality if the credible set contains zero. We derive the local asymptotic power of the tests under shrinking alternatives, and also present a simulation study to compare the finite-sample performance of our testing procedures with existing parametric and non-parametric tests.
