Jian Yan, Zhuoxi Li, Xianyang Zhang
arXiv 15 Oct 2022 · Statistics — Methodology
arXiv:2210.08149 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Wang, X., Pan, W., Hu, W., Tian, Y., and Zhang, H (2015) Conditional distance correlation | 1.000 | 14 | 4 | 100% |
| 2 | Ke, C. and Yin, X (2020) Expected conditional characteristic function-based measures for testing independence | 1.000 | 11 | 4 | 100% |
| 3 | Székely, G. J., Rizzo, M. L., et al (2004) Testing for equal distributions in high dimension | 1.000 | 6 | 3 | 100% |
| 4 | Gretton, A., Borgwardt, K. M., Rasch, M. J., Schölkopf, B., and Smol… (2012) A kernel two-sample test | 0.969 | 11 | 7 | 91% |
| 5 | Hu, X. and Lei, J (2024) A two-sample conditional distribution test using conformal prediction and weighted rank sum | 0.874 | 7 | 2 | 100% |
| 6 | Stute, W (1991) Conditional u-statistics | 0.874 | 5 | 2 | 100% |
| 7 | Sejdinovic, D., Sriperumbudur, B., Gretton, A., and Fukumizu, K (2013) Equivalence of distance-based and rkhs-based statistics in hypothesis testing | 0.811 | 4 | 2 | 100% |
| 8 | Huang, M.-Y., Qin, J., and Huang, C.-Y (2024) Efficient data integration under prior probability shift | 0.737 | 3 | 2 | 100% |
| 9 | Lee, M.-j (2009) Non-parametric tests for distributional treatment effect for randomly censored responses | 0.737 | 3 | 2 | 100% |
| 10 | Tibshirani, R. J., Foygel Barber, R., Candes, E., and Ramdas, A (2019) Conformal prediction under covariate shift | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 69 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Machine-Learning-Assisted Comparison of Regression Functions | 0.405 | 1 | 1 |