A multivariate Kolmogorov-Smirnov test of goodness of fit

By Ana Justel, D. Pena, Ruben H. Zamar. 1997

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Citations in the corpus

Spectral Density Ratio Models for Multivariate Extremes (2014, methodology): “In principle it would be natural to extend (16) to the Ddimensional setting by replacing the sup-norm with the multivariate Kolmogorov–Smirnov statistic of Justel, Peña, and Zamar (1997), though its computation seems difficult for D > 2.”
On tests for multivariate normality and associated simulation studies (2007, methodology): “[24] introduced a distribution-free multivariate Kolmogorov–Smirnov test and developed an algorithm to compute the associated statistic in the bivariate case.”
An empirical goodness-of-fit test for multivariate distributions (2013, methodology): “Proposals for extending the Kolmogorov–Smirnov goodnessof-fit test to multiple dimensions have been published [4,6,9,18], but the required test statistic in each proposed method is extremely difficult to compute, even in the bivariate case, and a suggested simplification in [6] still requires a tran”
The evaluation of Network Anomaly Detection Systems: Statistical analysis of the UNSW-NB15 data set and the comparison with the KDD99 data set (2016, methodology): “First, the Kolmogorov-Smirnov Test (Justel, Peña, & Zamar, 1997; Massey, 1951) defines and compares the distribution of the training and testing sets; skewness (Mardia, 1970) measures the asymmetry of the features; and kurtosis (Mardia, 1970) estimates the flatness of the features.”
Quantum Generative Adversarial Networks for learning and loading random distributions (2019, methodology): “The Kolmogorov-Smirnov statistic [53, 54] is based on the (empirical) cumulative distribution functions P (X ≤ x) and Q (X ≤ x) and is given by”
Comparison of multivariate distributions using quantile-quantile plots and related tests (2014, background): “, Burke [8] and Justel, Peña and Zamar [20]) in the one-sample and the two-sample problems.”
Selecting Representative Data Sets (2012, background): “Generalization of the most cited goodness-of-fit test, the Kolmogorov-Smirnov test, is in [10, 35, 54].”