Central limit theorem for Wasserstein projection - the case of convex order
Abstract
The main focuses of the article are limit theorems of Wasserstein projection in the convex order which are useful for inference tasks. The main results rely on the establishment of dual attainment, stability and several useful observations. The first is a clean criterion to invoke the Wasserstein projection dualities on the classical cost c=h(x−y). A new strategy was introduced to establish the dual attainment. Backward and forward dual transport are proved to enjoy a conjugate relationship. Sufficient conditions are given that ensure uniqueness of the optimal dual potential. These ingredients laid the groundwork for the proof of optimal dual potential stability, thereby permitting us to prove the central limit theorems under mild moment assumptions. Additional discussions show that the moment assumptions are sharp. These results also answered several open questions raised by Professor Benjamin Jourdain.
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BibTeX
@misc{ruan2026central,
title = {{Central limit theorem for Wasserstein projection - the case of convex order}},
author = {Yuanlong Ruan},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29565},
eprint = {2608.29565},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29565},
}
RIS
TY - UNPB
TI - Central limit theorem for Wasserstein projection - the case of convex order
AU - Yuanlong Ruan
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29565
UR - https://arxiv.org/abs/2608.29565
AB - The main focuses of the article are limit theorems of Wasserstein projection in the convex order which are useful for inference tasks. The main results rely on the establishment of dual attainment, stability and several useful observations. The first is a clean criterion to invoke the Wasserstein projection dualities on the classical cost c=h(x−y). A new strategy was introduced to establish the dual attainment. Backward and forward dual transport are proved to enjoy a conjugate relationship. Sufficient conditions are given that ensure uniqueness of the optimal dual potential. These ingredients laid the groundwork for the proof of optimal dual potential stability, thereby permitting us to prove the central limit theorems under mild moment assumptions. Additional discussions show that the moment assumptions are sharp. These results also answered several open questions raised by Professor Benjamin Jourdain.
ER -