A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space

Munsik Kim

We study the minimax rate of estimating a future value $\hat{I}{¼}_{t_n+h}$ of a curve $t\mapsto \hat{I}{¼}_t$ in the $2$-Wasserstein space ${\mathcal{P}}_2({\mathbb{R}}^d)$ from finitely many noisy sn…