In this paper, using the notion of data depth, we describe two classes of affine invariant test statistics for the one-sample location problem. The tests are implemented through the idea of permutation tests. The performance of the test against some competitors is investigated with an extensive simulation study. It is observed that the tests perform well when compared to their competitors for a wide spectrum of alternatives. If the proposed test is defined based on a moment-free depth function, then it is not inherently required to have finite moments of any order and the tests have broader applicability than some of the existing tests. The robustness property of the proposed tests is considered with a simulation study. Finally, we apply the tests to a real data example.

中文翻译：

---

多变量定位问题的基于非参数深度的测试

在本文中，使用数据深度的概念，我们描述了单样本位置问题的两类仿射不变测试统计量。这些测试是通过置换测试的思想实现的。通过广泛的模拟研究来研究针对某些竞争对手的测试性能。据观察，与竞争对手相比，这些测试在广泛的替代品方面表现良好。如果建议的测试是基于无矩深度函数定义的，那么它本身就不需要具有任何阶的有限矩，并且这些测试比一些现有测试具有更广泛的适用性。通过模拟研究考虑了所提出的测试的稳健性特性。最后，我们将测试应用于真实数据示例。