标题： 重访空间统计中的随机位移方法用于测试 显示英文标题

标题： Revisiting the random shift approach for testing in spatial statistics

摘要： 我们研究了平稳双变量空间过程的两个分量独立性非参数检验问题。 特别是，我们重新审视了随机位移方法，该方法已成为空间统计学中测试独立叠加假设的标准方法，并且在众多实际应用中被广泛使用。 然而，由于环面校正破坏了边缘空间相关结构，这种方法存在由自由度过高引起的问题。 这确实导致了蒙特卡洛检验精确性所必需的可交换性假设未得到满足。 我们提出了多种置换策略，并表明与环面校正相比，在随机场情况下，带方差校正的随机位移带来了适当的改进。 它降低了自由度过高的问题，并从所有研究的变体中获得了最大的功效。 为了获得方差校正方法的方差，研究了几种方法。 对于样本协方差作为检验统计量的情况，使用校正因子 $1/n$获得了最佳结果。 这对应于检验统计量方差的渐近阶数。 在点过程情况下，偏离可交换性的复杂性更高，我们提出了一种基于均值交叉最近邻距离和环面校正的替代策略。 它降低了自由度过高的问题，但比通常的交叉 $K$-函数获得的功效稍低。 因此，当点模式呈现聚类时，我们建议使用该方法，因为在这种情况下，交叉 $K$-函数会导致自由度过高的问题。 显示英文摘要

摘要： We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become a standard method for testing the independent superposition hypothesis in spatial statistics, and it is widely used in a plethora of practical applications. However, this method has a problem of liberality caused by breaking the marginal spatial correlation structure due to the toroidal correction. This indeed causes that the assumption of exchangability, which is essential for the Monte Carlo test to be exact, is not fulfilled. We present a number of permutation strategies and show that the random shift with the variance correction brings a suitable improvement compared to the torus correction in the random field case. It reduces the liberality and achieves the largest power from all investigated variants. To obtain the variance for the variance correction method, several approaches were studied. The best results were achieved, for the sample covariance as the test statistics, with the correction factor $1/n$. This corresponds to the asymptotic order of the variance of the test statistics. In the point process case, the problem of deviations from exchangeability is far more complex and we propose an alternative strategy based on the mean cross nearest-neighbor distance and torus correction. It reduces the liberality but achieves slightly lower power than the usual cross $K$-function. Therefore we recommend it, when the point patterns are clustered, where the cross $K$-function achieves liberality.