Multidimensional Stochastic Dominance Test Based on Center-outward Quantiles
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| Format: | Preprint |
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2025
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| _version_ | 1866915692259835904 |
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| author | Ma, Yiming Liu, Hang Zhuang, Weiwei |
| author_facet | Ma, Yiming Liu, Hang Zhuang, Weiwei |
| contents | Stochastic dominance (SD) provides a quantile-based partial ordering of random variables and has broad applications. Its extension to multivariate settings, however, is challenging due to the lack of a canonical ordering in $\mathbb{R}^d$ ($d \ge 2$) and the set-valued character of multivariate quantiles. Based on the multivariate center-outward quantile function in Hallin et al. (2021), this paper proposes new first- and second-order multivariate stochastic dominance (MSD) concepts through comparing contribution functions defined over quantile contours and regions. To address computational and inferential challenges, we incorporate entropy-regularized optimal transport, which ensures faster convergence rate and tractable estimation. We further develop consistent Kolmogorov-Smirnov and Cramér- von Mises type test statistics for MSD, establish bootstrap validity, and demonstrate through extensive simulations good finite-sample performance of the tests. Our approach offers a theoretically rigorous, and computationally feasible solution for comparing multivariate distributions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_19966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multidimensional Stochastic Dominance Test Based on Center-outward Quantiles Ma, Yiming Liu, Hang Zhuang, Weiwei Methodology Applications Stochastic dominance (SD) provides a quantile-based partial ordering of random variables and has broad applications. Its extension to multivariate settings, however, is challenging due to the lack of a canonical ordering in $\mathbb{R}^d$ ($d \ge 2$) and the set-valued character of multivariate quantiles. Based on the multivariate center-outward quantile function in Hallin et al. (2021), this paper proposes new first- and second-order multivariate stochastic dominance (MSD) concepts through comparing contribution functions defined over quantile contours and regions. To address computational and inferential challenges, we incorporate entropy-regularized optimal transport, which ensures faster convergence rate and tractable estimation. We further develop consistent Kolmogorov-Smirnov and Cramér- von Mises type test statistics for MSD, establish bootstrap validity, and demonstrate through extensive simulations good finite-sample performance of the tests. Our approach offers a theoretically rigorous, and computationally feasible solution for comparing multivariate distributions. |
| title | Multidimensional Stochastic Dominance Test Based on Center-outward Quantiles |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2512.19966 |