We address the problem of testing exchangeability and sign-invariant exchangeability based on one-dimensional projections. For that purpose, we first characterize those distributions that are (sign-invariant) exchangeable in terms of their one-dimensional projections. Based on these results, we propose new test procedures that are powerful, computationally efficient, and that circumvent the curse of dimensionality. We compare our procedure with some previous proposals in a small simulation study. Some of the results can be extended to the case of infinite-dimensional spaces (multivariate functional data).

翻译：我们处理基于一维预测的测试互换性和信号-变量互换性问题,为此,我们首先从单维预测的角度来描述那些(信号-变量)可互换的分布。根据这些结果,我们提出新的测试程序,这些程序是强大、计算效率高、能绕过维度诅咒的。我们将我们的程序与以前在小型模拟研究中的一些提议进行比较。有些结果可以扩展到无限维空间(多维功能数据)的情况。