Xiao Fang

activity

20092026

most citedFrom Stein identities to moderate deviations

37 citations · 164 across the 26 of their papers we have counts for

collaborators

27 papers

math.PR2026

Sharp Fourth-Moment Wasserstein CLT Bounds

Xiao Fang, Zi-Yao Su, Jiaxue Wang +1

We prove that for the normalized sum $W = \sum_{i = 1}^{n} X_{i} / n$ of independent, mean-zero, $d$ -dimensional random vectors with $\operatorname{Cov}(W) =Σ=\operatorname{diag}(σ_1^…

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★ 5 cited

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…

math.PR2020★ 1 cited

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…

math.ST2020★ 2 cited

Detection and Estimation of Local Signals

Xiao Fang, David Siegmund

We study the maximum score statistic to detect and estimate local signals in the form of change-points in the level, slope, or other property of a sequence of observations, and to…

math.PR2020

New error bounds in multivariate normal approximations via exchangeable pairs with applications to Wishart matrices and fourth moment theorems

Xiao Fang, Yuta Koike

We extend Stein's celebrated Wasserstein bound for normal approximation via exchangeable pairs to the multi-dimensional setting. As an intermediate step, we exploit the symmetry of…

math.PR2020

Arcsine laws for random walks generated from random permutations with applications to genomics

Xiao Fang, Han Liang Gan, Susan Holmes +4

A classical result for the simple symmetric random walk with $2 n$ steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the…

math.PR2020★ 8 cited

High-dimensional Central Limit Theorems by Stein's Method

Xiao Fang, Yuta Koike

We obtain explicit error bounds for the $d$ -dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling…

math.PR2019★ 1 cited

Skewness correction in tail probability approximations for sums of local statistics

Xiao Fang, Li Luo, Qi-Man Shao

Correcting for skewness can result in more accurate tail probability approximations in the central limit theorem for sums of independent random variables. In this paper, we extend…

math.PR2018★ 4 cited

Wasserstein-2 bounds in normal approximation under local dependence

Xiao Fang

We obtain a general bound for the Wasserstein-2 distance in normal approximation for sums of locally dependent random variables. The proof is based on an asymptotic expansion for e…

math.PR2018

Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula

Xiao Fang, Qi-Man Shao, Lihu Xu

Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for…

math.PR2017★ 6 cited

Limit theorems with rate of convergence under sublinear expectations

Xiao Fang, Shige Peng, Qi-Man Shao +1

Under the sublinear expectation $E [\cdot] := sup_{θ \in Θ} E_{θ} [\cdot]$ for a given set of linear expectations ${E_{θ} : θ \in Θ}$ , we establish a new law of large numbers and…

math.ST2016★ 3 cited

Segmentation and Estimation of Change-point Models: False Positive Control and Confidence Regions

Xiao Fang, Jian Li, David Siegmund

To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statist…

math.PR2014★ 1 cited

A universal error bound in the CLT for counting monochromatic edges in uniformly colored graphs

Xiao Fang

Let ${G_{n} : n \geq 1}$ be a sequence of simple graphs. Suppose $G_{n}$ has $m_{n}$ edges and each vertex of $G_{n}$ is colored independently and uniformly at random with $c_{n}$ colors. Re…

math.PR2014

A multivariate CLT for bounded decomposable random vectors with the best known rate

Xiao Fang

We prove a multivariate central limit theorem with explicit error bound on a non-smooth function distance for sums of bounded decomposable $d$ -dimensional random vectors. The decom…

math.PR2014★ 1 cited

Poisson approximation for two scan statistics with rates of convergence

Xiao Fang, David Siegmund

As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detectin…

math.PR2012★ 3 cited

Moderate deviations in Poisson approximation: a first attempt

Louis H. Y. Chen, Xiao Fang, Qi-Man Shao

Poisson approximation using Stein's method has been extensively studied in the literature. The main focus has been on bounding the total variation distance. This paper is a first a…

math.PR2012★ 17 cited

Rates of convergence for multivariate normal approximation with applications to dense graphs and doubly indexed permutation statistics

Xiao Fang, Adrian Röllin

We provide a new general theorem for multivariate normal approximation on convex sets. The theorem is formulated in terms of a multivariate extension of Stein couplings. We apply t…

math.PR2011★ 28 cited

Multivariate Normal Approximation by Stein's Method: The Concentration Inequality Approach

Louis H. Y. Chen, Xiao Fang

The concentration inequality approach for normal approximation by Stein's method is generalized to the multivariate setting. We use this approach to prove a non-smooth function dis…

Sharp Fourth-Moment Wasserstein CLT Bounds

Martingale central limit theorems in p-Wasserstein distance

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

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

From p-Wasserstein Bounds to Moderate Deviations

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

High order steady-state diffusion approximations

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

Normal Approximation and Fourth Moment Theorems for Monochromatic Triangles

Detection and Estimation of Local Signals

New error bounds in multivariate normal approximations via exchangeable pairs with applications to Wishart matrices and fourth moment theorems

Arcsine laws for random walks generated from random permutations with applications to genomics

High-dimensional Central Limit Theorems by Stein's Method

Skewness correction in tail probability approximations for sums of local statistics

Wasserstein-2 bounds in normal approximation under local dependence

Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula

Limit theorems with rate of convergence under sublinear expectations

Segmentation and Estimation of Change-point Models: False Positive Control and Confidence Regions

A universal error bound in the CLT for counting monochromatic edges in uniformly colored graphs

A multivariate CLT for bounded decomposable random vectors with the best known rate

Poisson approximation for two scan statistics with rates of convergence

Moderate deviations in Poisson approximation: a first attempt

Rates of convergence for multivariate normal approximation with applications to dense graphs and doubly indexed permutation statistics

Multivariate Normal Approximation by Stein's Method: The Concentration Inequality Approach

Martingale central limit theorems in $p$ -Wasserstein distance

From $p$ -Wasserstein Bounds to Moderate Deviations