219 citations · 1k across the 41 of their papers we have counts for
24 papers · 1 filter
Cramér's moderate deviations for martingales with applications
Xiequan Fan, Qi-Man Shao
Let be a sequence of martingale differences. Set and …
Cramér-type Moderate Deviation for Quadratic Forms with a Fast Rate
Xiao Fang, Song-Hao Liu, Qi-Man Shao
Let be independent and identically distributed random vectors in . Suppose , , where is the $d\times d…
Refined Cramér Type Moderate Deviation Theorems for General Self-normalized Sums with Applications to Dependent Random Variables and Winsorized Mean
Lan Gao, Qi-Man Shao, Jiasheng Shi
Let {(X_i,Y_i)}_{i=1}^n be a sequence of independent bivariate random vectors. In this paper, we establish a refined Cramér type moderate deviation theorem for the general self-nor…
Berry--Esseen Bounds for Multivariate Nonlinear Statistics with Applications to M-estimators and Stochastic Gradient Descent Algorithms
Qi-Man Shao, Zhuo-Song Zhang
We establish a Berry--Esseen bound for general multivariate nonlinear statistics by developing a new multivariate-type randomized concentration inequality. The bound is the best po…
A probability approximation framework: Markov process approach
Peng Chen, Qi-Man Shao, Lihu Xu
We view the classical Lindeberg principle in a Markov process setting to establish a probability approximation framework by the associated Itô's formula and Markov operator. As app…
Self-normalized Cramér type moderate deviations for stationary sequences and applications
Xiequan Fan, Ion Grama, Quansheng Liu +1
Let be a stationary sequence. Denote and where stands for the integer part of …