Related papers: Optimal Berry-Esseen bounds on the Poisson space
In this work we consider regularized Wasserstein barycenters (average in Wasserstein distance) in Fourier basis. We prove that random Fourier parameters of the barycenter converge to some Gaussian random vector by distribution. The…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
We introduce a new family of distributions to approximate $\mathbb {P}(W\in A)$ for $A\subset\{...,-2,-1,0,1,2,...\}$ and $W$ a sum of independent integer-valued random variables $\xi_1$, $\xi_2$, $...,$ $\xi_n$ with finite second moments,…
We establish some deviation inequalities, moment bounds and almost sure results for the Wasserstein distance of order p $\in$ [1, $\infty$) between the empirical measure of independent and identically distributed R d-valued random variables…
Non-asymptotic bounds for Gaussian and bootstrap approximation have recently attracted significant interest in high-dimensional statistics. This paper studies Berry-Esseen bounds for such approximations with respect to the multivariate…
We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the $L^2$-Wasserstein metric tensor in the probability density space to a parameter space, equipping the…
We study rates of convergence in central limit theorems for the partial sum of squares of general Gaussian sequences, using tools from analysis on Wiener space. No assumption of stationarity, asymptotically or otherwise, is made. The main…
We establish a general inequality on the Poisson space, yielding an upper bound for the distance in total variation between the law of a regular random variable with values in the integers and a Poisson distribution. Several applications…
Considering two random variables with different laws to which we only have access through finite size iid samples, we address how to reweight the first sample so that its empirical distribution converges towards the true law of the second…
Applying an inductive technique for Stein and zero bias couplings yields Berry-Esseen theorems for normal approximation for two new examples. The conditions of the main results do not require that the couplings be bounded. Our two…
Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study the multivariate Poisson approximation of the distribution…
Suppose that the (normalised) partial sum of a stationary sequence converges to a standard normal random variable. Given sufficiently moments, when do we have a rate of convergence of $n^{-1/2}$ in the uniform metric, in other words, when…
The inductive size bias coupling technique and Stein's method yield a Berry-Esseen theorem for the number of urns having occupancy $d \ge 2$ when $n$ balls are uniformly distributed over $m$ urns. In particular, there exists a constant $C$…
An analogue of the Berry-Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n^{-1/2}, the same as in the classical case.…
The main result of this work is the proof of the boundedness of the Ornstein-Uhlenbeck semigroup $ \{T_t \}_{t\geq 0} $ in $ {\mathbb R}^d $ on Gaussian variable Lebesgue spaces under a condition of regularity on $p(\cdot)$ following…
Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…
Continuing the analysis initiated in Lachi\'eze-Rey and Peccati (2011), we use contraction operators to study the normal approximation of random variables having the form of a U-statistic written on the points in the support of a random…
We expound on some known lower bounds of the quadratic Wasserstein distance between random vectors in $\mathbb{R}^n$ with an emphasis on affine transformations that have been used in manifold learning of data in Wasserstein space. In…
We derive a Gaussian Central Limit Theorem for the sample quantiles based on locally dependent random variables with explicit convergence rate. Our approach is based on converting the problem to a sum of indicator random variables, applying…