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On nonparametric conditional independence tests for continuous variables

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Abstract Testing conditional independence (CI) for continuous variables is a fundamental but challenging task in statistics. Many tests for this task are developed and used increasingly widely by data analysts. This article reviews the current status of the nonparametric part of these tests, which assumes no parametric form for the joint continuous density function. The different ways to approach the CI are summarized. Tests are also grouped according to their data assumptions and method types. A numerical comparison is also conducted for representative tests. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis > Multivariate Analysis
Test performance comparisons with post‐nonlinear noise model and similar setup as in Strobl et al. (). Shown are KS (left column), AUPC (center column), and runtime (right column) for an experiment with dZ = 1 (top row), dZ = 5 (middle row), and dZ = 10 (bottom row). The original CPU time t is transformed in this way, log(t + 1), for calculating runtime. The horizontal axis corresponds to the sample size. Error bars give the bootstrapped standard errors. AUPC, area under the power curve; KS, Kolmogorov–Smirnov
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Statistical and Graphical Methods of Data Analysis > Multivariate Analysis
Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data

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