Xiao Fang

activity

20182026

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

2 citations · 3 across the 7 of their papers we have counts for

collaborators

11 papers

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

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

Large-dimensional Central Limit Theorem with Fourth-moment Error Bounds on Convex Sets and Balls

Xiao Fang, Yuta Koike

We prove the large-dimensional Gaussian approximation of a sum of $n$ independent random vectors in $R^{d}$ together with fourth-moment error bounds on convex sets and Eucli…

math.PR2020

Normal Approximation and Fourth Moment Theorems for Monochromatic Triangles

Bhaswar B. Bhattacharya, Xiao Fang, Han Yan

Given a graph sequence ${G_{n}}_{n \geq 1}$ denote by $T_{3} (G_{n})$ the number of monochromatic triangles in a uniformly random coloring of the vertices of $G_{n}$ with $c \geq 2$ color…

Martingale central limit theorems in p-Wasserstein distance