Wenxi Tan, Bing Li, Lingzhou Xue
arXiv 31 Jul 2026 · Statistics — Methodology
arXiv:2607.28981 · PDF · Extracted main text
Testing independence or conditional independence is fundamental to statistical inference, yet existing methods for non-Euclidean random objects often face a difficult trade-off between geometric flexibility and theoretical tractability. We introduce the Distance Profile Embedding (DPE), a novel representation that maps random objects from general metric spaces into a Hilbert space of square-integrable functions. We prove that this mapping is injective and preserves full distributional information without requiring isometric Hilbert embeddings or one-to-one correspondence conditions. Leveraging the DPE, we develop a unified framework for marginal and conditional independence testing of random objects that enjoys a rigorous asymptotic theory for both size and power. Notably, our framework is the first in the literature to accommodate object-valued conditioning variables when testing conditional independence, overcoming the Euclidean or Hilbertian constraints of existing methodologies. We facilitate the calculation of analytic $p$-values using closed-form asymptotic null distributions, which avoids the computational burden of permutation tests common in existing metric-based methods. The numerical properties of our methods are demonstrated through both simulations and two real-world applications involving gut microbiome compositions and global human mortality distributions, respectively.
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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 | Zhou, Hang and Müller, Hans-Georg (2026) Association and independence test for random objects | 1.000 | 16 | 6 | 100% |
| 2 | Zhang, Kun and Peters, Jonas and Janzing, Dominik and Schölkopf, Ber… (2011) Kernel-based conditional independence test and application in causal discovery | 1.000 | 12 | 3 | 100% |
| 3 | Chen, Yaqing and Dubey, Paromita (2026) Testing mutual independence in metric spaces using distance profiles | 1.000 | 9 | 4 | 100% |
| 4 | Gretton, Arthur and Fukumizu, Kenji and Teo, Choon and Song, Le and… (2007) A kernel statistical test of independence | 1.000 | 9 | 3 | 100% |
| 5 | Wang, Xueqin and Zhu, Jin and Pan, Wenliang and Zhu, Junhao and Zhan… (2024) Nonparametric statistical inference via metric distribution function in metric spaces | 1.000 | 8 | 4 | 100% |
| 6 | Gábor J. Székely and Maria L. Rizzo and Nail K. Bakirov (2007) Measuring and testing dependence by correlation of distances | 0.811 | 4 | 2 | 100% |
| 7 | Gary D. Wu and Jun Chen and Christian Hoffmann and Kyle Bittinger an… (2011) Linking long-term dietary patterns with gut microbial enterotypes | 0.737 | 3 | 2 | 100% |
| 8 | Christensen, Jens Peter Reus (1970) On some measures analogous to Haar measure. | 0.737 | 3 | 2 | 100% |
| 9 | Hoffmann-Jorgensen, J (1975) Measures which agree on balls. | 0.737 | 3 | 2 | 100% |
| 10 | Bing Li (2018) Linear operator-based statistical analysis: a useful paradigm for big data self | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 43 scored citations.