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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.02700 |
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| _version_ | 1866910241866645504 |
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| author | Yordanov, Alexander Hristov, Peter |
| author_facet | Yordanov, Alexander Hristov, Peter |
| contents | We develop Wasserstein-based hypothesis tests for empirical-measure convergence in stationary dependent sequences. For a known candidate invariant measure, $μ$, we study the statistic $T_n=\sqrt{n}\,W_1(\hatμ_n,μ)$ and establish asymptotic level-$α$ validity under the null, together with consistency under fixed alternatives. When the invariant measure is unknown, we derive the asymptotic law of the pairwise statistic $\sqrt{n}\,W_1(\hatμ_n^{(i)},\hatμ_n^{(j)})$ for independent trajectories and obtain a corresponding pairwise test, including Bonferroni control for multiple comparisons. To make this estimation feasible when the long-run covariance is unavailable in closed form, we introduce a finite-grid plug-in estimator and show that Gaussian critical values based on the estimated covariance consistently recover the corresponding oracle fixed-grid estimation. Simulation experiments in both linear and nonlinear dynamical settings illustrate the oracle and plug-in regimes, along with the resulting coverage probability and power. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02700 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wasserstein-Based Test for Empirical Measure Convergence of Dependent Sequences Yordanov, Alexander Hristov, Peter Applications We develop Wasserstein-based hypothesis tests for empirical-measure convergence in stationary dependent sequences. For a known candidate invariant measure, $μ$, we study the statistic $T_n=\sqrt{n}\,W_1(\hatμ_n,μ)$ and establish asymptotic level-$α$ validity under the null, together with consistency under fixed alternatives. When the invariant measure is unknown, we derive the asymptotic law of the pairwise statistic $\sqrt{n}\,W_1(\hatμ_n^{(i)},\hatμ_n^{(j)})$ for independent trajectories and obtain a corresponding pairwise test, including Bonferroni control for multiple comparisons. To make this estimation feasible when the long-run covariance is unavailable in closed form, we introduce a finite-grid plug-in estimator and show that Gaussian critical values based on the estimated covariance consistently recover the corresponding oracle fixed-grid estimation. Simulation experiments in both linear and nonlinear dynamical settings illustrate the oracle and plug-in regimes, along with the resulting coverage probability and power. |
| title | Wasserstein-Based Test for Empirical Measure Convergence of Dependent Sequences |
| topic | Applications |
| url | https://arxiv.org/abs/2604.02700 |