6 papers · 1 filter
On the L{é}vy concentration function of Gaussian quadratic forms with applications to second order U-statistics
Abhimanyu Choudhary, Arun Kumar Kuchibhotla
We provide an upper-bound for the L{é}vy concentration function: where is a weighted sum…
Berry-Esseen bounds for multivariate martingale difference sequences in the Kolmogorov distance
Weichen Wu, Dung Le, Arun Kumar Kuchibhotla +1
We derive new Gaussian approximations for finite martingale difference sequences in with respect to the Kolmogorov distance. Under appropriate conditions, our bounds…
Dual Induction CLT for High-dimensional m-dependent Data
Heejong Bong, Arun Kumar Kuchibhotla, Alessandro Rinaldo
We derive novel and sharp high-dimensional Berry--Esseen bounds for the sum of -dependent random vectors over the class of hyper-rectangles exhibiting only a poly-logarithmic de…
Maximal Inequalities for Independent Random Vectors
Supratik Basu, Arun K Kuchibhotla
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric a…
The Berry-Esseen Bound for High-dimensional Self-normalized Sums
Woonyoung Chang, Kenta Takatsu, Konrad Urban +1
This manuscript studies the Gaussian approximation of the coordinate-wise maximum of self-normalized statistics in high-dimensional settings. We derive an explicit Berry-Esseen bou…
On the Missing Factor in Some Concentration Inequalities for Martingales
Arun Kumar Kuchibhotla
In this note, we improve some concentration inequalities for martingales with bounded increments. These results recover the missing factor in Freedman-style inequalities and are ne…