The assumption of separability is a simplifying and very popular assumption in the analysis of spatiotemporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for example, because of a small sample size or because of computational storage problems. In this paper we propose a new and very simple test to validate this assumption. Our approach is based on a measure of separability which is zero in the case of separability and positive otherwise. We derive the asymptotic distribution of a corresponding estimate under the null hypothesis and the alternative and develop an asymptotic and a bootstrap test which are very easy to implement. In particular, our approach does neither require projections on subspaces generated by the eigenfunctions of the covariance operator nor distributional assumptions as recently used by (Ann. Statist. 45 (2017) 1431–1461) and (Biometrika 104 425–437) to construct tests for separability. We investigate the finite sample performance by means of a simulation study and also provide a comparison with the currently available methodology. Finally, the new procedure is illustrated analyzing a data example.

中文翻译：

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随机曲面协方差算子中的可分离性检验

在时空或超表面数据结构的分析中，可分离性的假设是一种简化且非常普遍的假设。通常在无法轻易估计协方差结构的情况下（例如，由于样本量较小或由于计算存储问题）。在本文中，我们提出了一个新的非常简单的测试来验证这一假设。我们的方法基于可分离性的度量，在可分离性的情况下为零，否则为正。我们在原假设和替代条件下得出相应估计的渐近分布，并开发了非常易于实现的渐近和自举检验。尤其是，安 统计员。 45（2017）1431–1461）和（Biometrika 104 425–437）构建可分离性测试。我们通过模拟研究来调查有限的样本性能，并与当前可用的方法进行比较。最后，通过分析数据示例说明了新过程。