Related papers: New Kolmogorov bounds for functionals of binomial …
Let $ (Z_{n})_{n\geq 0} $ be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-$1$ distance for the process $ (Z_{n})_{n\geq 0} $,…
In this paper we use a Malliavin-Stein type method to investigate Poisson and normal approximations for the measurable functions of infinitely many independent random variables. We combine Stein's method with the difference operators in…
We study both the positively and negatively step-reinforced random walks with parameter $p$. For a step distribution $\mu$ with finite second moment, the positively step-reinforced random walk with $p\in [1/2,1)$ and the negatively…
We show how to detect optimal Berry--Esseen bounds in the normal approximation of functionals of Gaussian fields. Our techniques are based on a combination of Malliavin calculus, Stein's method and the method of moments and cumulants, and…
Berry-Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.
We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstein and the Kolmogorov distance of functionals of a general Poisson process (Poisson random measure). Our approach is based on an iteration of…
The Kolmogorov distances between a symmetric hypergeometric law with standard deviation $\sigma$ and its usual normal approximations are computed and shown to be less than $1/(\sqrt{8\pi}\,\sigma)$, with the order $1/\sigma$ and the…
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 possible for many known statistics. As applications,…
We obtain estimates for the Kolmogorov distance to appropriately chosen gaussians, of linear functions \[ \sum_{i\in [n]^d} \theta_i X_i \] of random tensors $\boldsymbol{X}=\langle X_i:i\in [n]^d\rangle$ which are symmetric and…
We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors. We establish higher-order approximation bounds with error terms depending on a sample size and a…
In the present paper we consider the Ornstein-Uhlenbeck process of the second kind defined as solution to the equation $dX_{t} = -\alpha X_{t}dt+dY_{t}^{(1)}, \ \ X_{0}=0$, where $Y_{t}^{(1)}:=\int_{0}^{t}e^{-s}dB^H_{a_{s}}$ with…
In his work \cite{Ti80}, Tikhomirov combined elements of Stein's method with the theory of characteristic functions to derive Kolmogorov bounds for the convergence rate in the central limit theorem for a normalized sum of a stationary…
We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non uniform bounds on these solutions (a.k.a.\ Stein factors). We use these…
In this paper, a simplified second-order Gaussian Poincar\'e inequality for normal approximation of functionals over infinitely many Rademacher random variables is derived. It is based on a new bound for the Kolmogorov distance between a…
We obtain new bounds for the solution of the variance-gamma (VG) Stein equation that are of the correct form for approximations in terms of the Wasserstein and Kolmorogorov metrics. These bounds hold for all parameters values of the four…
In this paper, we establish Berry--Esseen bounds for both self-normalized and non-self-normalized sums of locally dependent random variables. The proofs are based on Stein's method together with a concentration inequality approach. We…
We consider solutions of stochastic differential equations which diverge to infinity as the time parameter goes to infinity. If the coefficients converge as the spacial variable goes to infinity, then the solutions will get close to some…
In this paper, moderate deviations for normal approximation of functionals over infinitely many Rademacher random variables are derived. They are based on a bound for the Kolmogorov distance between a general Rademacher functional and a…
New nonuniform Berry--Esseen-type bounds for sums of independent random variables are obtained, motivated by recent studies concerning such bounds for nonlinear statistics. The proofs are based on the Chen--Shao concentration techniques…
We prove that the sum of $t$ boolean-valued random variables sampled by a random walk on a regular expander converges in total variation distance to a discrete normal distribution at a rate of $O(\lambda/t^{1/2-o(1)})$, where $\lambda$ is…