6 papers
Quantitative bounds for high dimensional entropic CLT
Chang-song Deng, Lin Wang, Lihu Xu
By extending the Johnson--Barron projection method from one dimension to high dimensions and utilizing a Wang type dimension-free Harnack inequality, we obtain a new quantitative b…
Berry-Esseen Bounds and Moderate Deviations for Catoni-Type Robust Estimation
Zhijun Cai, Xiang Li, Lihu Xu
A powerful robust mean estimator introduced by Catoni (2012) allows for mean estimation of heavy-tailed data while achieving the performance characteristics of classical mean estim…
Tuning free Catoni type joint robust estimation
Xiang Li, Jun S. Liu, Qiang Sun +1
This paper develops a Catoni-type joint (tuning-free) estimation framework for parametric models with heavy-tailed noise, in which the target parameter and the unknown noise varian…
Total variation distance between SDEs with stable noise and Brownian motion
Changsong Deng, Xiang Li, Rene L. Schilling +1
We consider a -dimensional stochastic differential equation (SDE) of the form , let be the solution if the driving noise is a -dimen…
Stable central limit theorem in total variation distance
Xiang Li, Lihu Xu, Haoran Yang
Under certain general conditions, we prove that the stable central limit theorem holds in the total variation distance and get its optimal convergence rate for all . Ou…
Unadjusted Langevin Algorithms for SDEs with Hoelder Drift
Xiang Li, Feng-Yu Wang, Lihu Xu
Consider the following stochastic differential equation for on and its Euler-Maruyama (EM) approximation : \begin{align…