3 papers
math.ST2019
Estimation of Wasserstein distances in the Spiked Transport Model
Jonathan Niles-Weed, Philippe Rigollet
We propose a new statistical model, the spiked transport model, which formalizes the assumption that two probability distributions differ only on a low-dimensional subspace. We stu…
math.ST2019
Convergence of Smoothed Empirical Measures with Applications to Entropy Estimation
Ziv Goldfeld, Kristjan Greenewald, Yury Polyanskiy +1
This paper studies convergence of empirical measures smoothed by a Gaussian kernel. Specifically, consider approximating , for $\mathcal{N}_σ\triangleq\mathcal{…
math.ST2019
Minimax estimation of smooth densities in Wasserstein distance
Jonathan Niles-Weed, Quentin Berthet
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics an…