3 papers
math.ST2020
Optimal Rates for Estimation of Two-Dimensional Totally Positive Distributions
Jan-Christian Hütter, Cheng Mao, Philippe Rigollet +1
We study minimax estimation of two-dimensional totally positive distributions. Such distributions pertain to pairs of strongly positively dependent random variables and appear freq…
math.ST2019
Minimax estimation of smooth optimal transport maps
Jan-Christian Hütter, Philippe Rigollet
Brenier's theorem is a cornerstone of optimal transport that guarantees the existence of an optimal transport map between two probability distributions and over $\mathb…
math.ST2016
Optimal rates for total variation denoising
Jan-Christian Hütter, Philippe Rigollet
Motivated by its practical success, we show that the two-dimensional total variation denoiser satisfies a sharp oracle inequality that leads to near optimal rates of estimation for…