Xiao Fang

activity

20162026

most citedCramér-type Moderate Deviation for Quadratic Forms with a Fast Rate

2 citations · 3 across the 8 of their papers we have counts for

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Showing math.PRShow all

15 papers · 1 filter

math.PR2026

Martingale central limit theorems in $p$ -Wasserstein distance

Xiao Fang, Yuta Koike, Zi-Yao Su

We obtain multivariate martingale central limit theorems in $p$ -Wasserstein distance with respect to the $ℓ_{r}$ norm in $R^{d}$ for $p \geq 1$ and $r \in [1, \infty]$ , which…

math.PR2023

High-dimensional Central Limit Theorems by Stein's Method in the Degenerate Case

Xiao Fang, Yuta Koike, Song-Hao Liu +1

In the literature of high-dimensional central limit theorems, there is a gap between results for general limiting correlation matrix $Σ$ and the strongly non-degenerate case. For t…

math.PR2022

Sharp High-dimensional Central Limit Theorems for Log-concave Distributions

Xiao Fang, Yuta Koike

Let $X_{1}, \dots, X_{n}$ be i.i.d. log-concave random vectors in $R^{d}$ with mean 0 and covariance matrix $Σ$ . We study the problem of quantifying the normal approximation error…

math.PR2022

From $p$ -Wasserstein Bounds to Moderate Deviations

Xiao Fang, Yuta Koike

We use a new method via $p$ -Wasserstein bounds to prove Cramér-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized…

math.PR2021★ 2 cited

Cramér-type Moderate Deviation for Quadratic Forms with a Fast Rate

Xiao Fang, Song-Hao Liu, Qi-Man Shao

Let $X_{1}, \dots, X_{n}$ be independent and identically distributed random vectors in $R^{d}$ . Suppose $E X_{1} = 0$ , $Cov (X_{1}) = I_{d}$ , where $I_{d}$ is the $d\times d…

math.PR2020

High order steady-state diffusion approximations

Anton Braverman, J. G. Dai, Xiao Fang

We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chai…

Martingale central limit theorems in p-Wasserstein distance