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Distance and Kernel-Based Measures for Global and Local Two-Sample Conditional Distribution Testing

Jian Yan, Zhuoxi Li, Xianyang Zhang

arXiv 15 Oct 2022 · Statistics — Methodology

arXiv:2210.08149 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention in the literature, with existing works focusing exclusively on global two-sample conditional distribution testing. Based on distance and kernel methods, this paper presents the first unified framework for both global and local two-sample conditional distribution testing. To this end, we introduce distance and kernel-based measures that characterize the homogeneity of two conditional distributions. Drawing from the concept of conditional U-statistics, we propose consistent estimators for these measures. Theoretically, we derive the convergence rates and the asymptotic distributions of the estimators under both the null and alternative hypotheses. Utilizing these measures, along with a local bootstrap approach, we develop global and local tests that can detect discrepancies between two conditional distributions at global and local levels, respectively. Our tests demonstrate reliable performance through simulations and real data analysis.

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69
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143
in-text mentions
69
distinct cited
3
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11,599
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Wang, X., Pan, W., Hu, W., Tian, Y., and Zhang, H (2015) Conditional distance correlation1.000144100%
2Ke, C. and Yin, X (2020) Expected conditional characteristic function-based measures for testing independence1.000114100%
3Székely, G. J., Rizzo, M. L., et al (2004) Testing for equal distributions in high dimension1.00063100%
4Gretton, A., Borgwardt, K. M., Rasch, M. J., Schölkopf, B., and Smol… (2012) A kernel two-sample test0.96911791%
5Hu, X. and Lei, J (2024) A two-sample conditional distribution test using conformal prediction and weighted rank sum0.87472100%
6Stute, W (1991) Conditional u-statistics0.87452100%
7Sejdinovic, D., Sriperumbudur, B., Gretton, A., and Fukumizu, K (2013) Equivalence of distance-based and rkhs-based statistics in hypothesis testing0.81142100%
8Huang, M.-Y., Qin, J., and Huang, C.-Y (2024) Efficient data integration under prior probability shift0.73732100%
9Lee, M.-j (2009) Non-parametric tests for distributional treatment effect for randomly censored responses0.73732100%
10Tibshirani, R. J., Foygel Barber, R., Candes, E., and Ramdas, A (2019) Conformal prediction under covariate shift0.73732100%

Showing the top 10 of 69 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Machine-Learning-Assisted Comparison of Regression Functions0.40511