A Distribution Free Version of the Smirnov Two Sample Test in the $p$-Variate Case

By Peter J. Bickel. 1969

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Citations in the corpus

Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, background): “While there has been work on generalizing these popular one-dimensional to higher dimensions, like Bickel [1969], these are seemingly not the most common multivariate tests.”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, background): “This task, however, is very difficult and challenging in practice since the underneath distribution information are generally unknown apriori (Bickel, 1969; Friedman & Rafsky, 1979; Hall & Tajvidi, 2002; Biau & Gyofi, 2005).”
On the empirical estimation of integral probability metrics (2012, methodology): “In statistics, IPMs have been used in nonparametric two-sample testing, including the Kolmogorov-Smirnov test [7, 39, 40] and the kernel test [20, 21]; as well as in independence testing [20, Section 7.”
A Kernel Method for the Two-Sample-Problem (2006, methodology): “Two possible generalisations of the Kolmogorov-Smirnov test t o the multivariate case were studied in [4, 12].”
Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds (2008, background): “In the statistical literature, measures of scatter and spread have been discussed by Bickel and Lehmann (1979), Oja (1983) and Shaked and Shanthikumar 1994), among others.”
Matching shapes (2001, background): “2Alternatives include Bickel’s generalization of the KolmogorovSmirnov test for 2D distributions [4], which does not require binning.”
Shape Matching and Object Recognition Using Shape Contexts (2002, methodology): “In our experiments, we use the (3)Alternatives include Bickel's generalization of the Kolmogorov-Smirnov test for 2D distributions [4], which does not require binning.”
Matching with shape contexts (2000, methodology): “This is particularly useful when we are comparing shapes derived from gray-level images instead of (5)Alternatives include Bickel’s generalization of the Kolmogorov-Smirnov test for 2D distributions [7], which does not require binning, or treating the shape contexts as vectors and comparing them usi”
Assessing the Calibration of High-Dimensional Ensemble Forecasts Using Rank Histograms (2013, methodology): “25 In the case of a univariate probabilistic forecast given by a continuous predictive distribution, 26 Dawid (1984) proposes the use of the probability integral transform (PIT) for calibration assess27 ment.”
Integrating structured biological data by Kernel Maximum Mean Discrepancy (2006, methodology): “Two possible generalizations of the Kolmogorov-Smirnov test to the multivariate case were studied by Bickel (1969); Friedman and Rafsky (1979).”
TESTING FOR EQUAL DISTRIBUTIONS IN HIGH DIMENSION (2004, methodology): “Bickel (1969) constructed a consistent distribution free multivariate extension of the univariate Smirnov test by conditioning on the pooled sample.”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, unknown): “, [16, 152], [73] and the references therein).”