Wasserstein Concentration of Empirical Measures for Dependent Data via the Method of Moments
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917195883216896 |
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| author | Amini, Arash A. Vinas, Luciano |
| author_facet | Amini, Arash A. Vinas, Luciano |
| contents | We establish a general concentration result for the 1-Wasserstein distance between the empirical measure of a sequence of random variables and its expectation. Unlike standard results that rely on independence (e.g., Sanov's theorem) or specific mixing conditions, our result requires only two conditions: (1) control over the variance of the empirical moments, and (2) a flexible tail condition we term $Ψ_{r_n}$-sub-Gaussianity. This approach allows for significant dependencies between variables, provided their algebraic moments behave predictably. The proof uses the method of moments combined with a polynomial approximation of Lipschitz functions via Jackson kernels, allowing us to translate moment concentration into topological concentration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07228 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wasserstein Concentration of Empirical Measures for Dependent Data via the Method of Moments Amini, Arash A. Vinas, Luciano Statistics Theory We establish a general concentration result for the 1-Wasserstein distance between the empirical measure of a sequence of random variables and its expectation. Unlike standard results that rely on independence (e.g., Sanov's theorem) or specific mixing conditions, our result requires only two conditions: (1) control over the variance of the empirical moments, and (2) a flexible tail condition we term $Ψ_{r_n}$-sub-Gaussianity. This approach allows for significant dependencies between variables, provided their algebraic moments behave predictably. The proof uses the method of moments combined with a polynomial approximation of Lipschitz functions via Jackson kernels, allowing us to translate moment concentration into topological concentration. |
| title | Wasserstein Concentration of Empirical Measures for Dependent Data via the Method of Moments |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2601.07228 |