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A distribution-free multivariate Kolmogorov–Smirnov goodness of fit test has been proposed by Justel, Peña and Zamar (1997). The test uses a statistic which is built using Rosenblatt's transformation, and an algorithm is developed to compute it in the bivariate case.  An approximate test that can be easily computed in any dimension is also presented.

A distribution-free multivariate Kolmogorov–Smirnov goodness of fit test has been proposed by Justel, Peña and Zamar (1997). The test uses a statistic which is built using Rosenblatt's transformation, and an algorithm is developed to compute it in the bivariate case.  An approximate test that can be easily computed in any dimension is also presented.

Justel，Peña和Zamar（1997）提出了无分布的多元Kolmogorov-Smirnov拟合优度检验。该检验使用通过Rosenblatt变换建立的统计量，开发出了一种算法来计算双变量情况。还介绍了可以在任何维度上轻松计算的近似检测法。

朱斯特尔 Justel，培尼亚 Peña和扎马 Zamar（1997）提出了无分布的多元Kolmogorov-Smirnov拟合优度检验。该检验使用通过Rosenblatt变换建立的统计量，开发出了一种算法来计算双变量情况。还介绍了可以在任何维度上轻松计算的近似检测法。

One approach to generalizing the Kolmogorov–Smirnov statistic to higher dimensions which meets the above concern is to compare the cdfs of the two samples with all possible orderings, and take the largest of the set of resulting K–S statistics.  In ''d'' dimensions, there are 2^''d''−1 such orderings.  One such variation is due to Peacock(see also Gosset for a 3D version) and another to Fasano and Franceschini (see Lopes et al. for a comparison and computational details). Critical values for the test statistic can be obtained by simulations, but depend on the dependence structure in the joint distribution.

One approach to generalizing the Kolmogorov–Smirnov statistic to higher dimensions which meets the above concern is to compare the cdfs of the two samples with all possible orderings, and take the largest of the set of resulting K–S statistics.  In ''d'' dimensions, there are 2^''d''−1 such orderings.  One such variation is due to Peacock(see also Gosset for a 3D version) and another to Fasano and Franceschini (see Lopes et al. for a comparison and computational details). Critical values for the test statistic can be obtained by simulations, but depend on the dependence structure in the joint distribution.

在满足以上要求的同时，将Kolmogorov-Smirnov统计量泛化为更高维度的一种方法是，在所有可能的排序中比较两个样本的累积分布函数，并从所得的K-S统计量中取最大。在d维数据中，有2d-1个这样的排序。Peacock得出了一种这样的变化量（有关3D版本，另请参见Gosset），另一种由Fasano和Franceschini得出（有关比较和计算细节，请参见Lopes等人）。检测统计量的临界值可以通过仿真获取，但取决于联合分布中的依存关系结构。

在满足以上要求的同时，将Kolmogorov-Smirnov统计量泛化为更高维度的一种方法是，在所有可能的排序中比较两个样本的累积分布函数，并从所得的K-S统计量中取最大。在d维数据中，有2d-1个这样的排序。皮柯克  Peacock得出了一种这样的变化量（有关3D版本，另请参见Gosset），另一种由法萨诺 Fasano和弗朗切斯基尼 Franceschini得出（有关比较和计算细节，请参见Lopes等人）。检测统计量的临界值可以通过仿真获取，但取决于联合分布中的依存关系结构。