Related papers: Normal approximation for nonlinear statistics usin…
We prove concentration inequalities for several models of non-linear random matrices. As corollaries we obtain estimates for linear spectral statistics of the conjugate kernel of neural networks and non-commutative polynomials in (possibly…
Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics,…
This article presents a new proof of the rate of convergence to the normal distribution of sums of independent, identically distributed random variables in chi-square distance, which was also recently studied in \cite{BobkovRenyi}. Our…
It is often the case in Statistics that one needs to compute sums of infinite series, especially in marginalising over discrete latent variables. This has become more relevant with the popularization of gradient-based techniques (e.g.…
We deduce in this paper the sufficient conditions for weak convergence of centered and normed deviation of the u-statistics with values in the space of the real valued continuous function defined on some compact metric space. We obtain also…
We explore the applications of our previously established likelihood-ratio method for deriving concentration inequalities for a wide variety of univariate and multivariate distributions. New concentration inequalities for various…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration inequalities. It can be useful to obtain consistency…
We propose a new functional analytic approach to Stein's method of exchangeable pairs that does not require the pair at hand to satisfy any approximate linear regression property. We make use of this theory in order to derive abstract…
We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centred, of a random matrix with a variance profile and the standard Gaussian random variable. The second order Poincar\'e…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…
This paper is concerned with normal approximation under relaxed moment conditions using Stein's method. We obtain the explicit rates of convergence in the central limit theorem for (i) nonlinear statistics with finite absolute moment of…
Given an i.i.d. sample drawn from some probability distribution on a finite set, the best (in the sense of least variance) linear unbiased estimator (BLUE) of the average of any quantity with respect to that distribution is the sample…
We establish new lower bounds for the normal approximation in the Wasserstein distance of random variables that are functionals of a Poisson measure. Our results generalize previous findings by Nourdin and Peccati (2012, 2015) and Bierm\'e,…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…
We prove a Berry-Esseen bound in de Jong's classical CLT for normalized, completely degenerate $U$-statistics, which says that the convergence of the fourth moment sequence to three and a Lindeberg-Feller type negligibility condition are…
Let $(X_{n,t})_{t=1}^{\infty}$ be a stationary absolutely regular sequence of real random variables with the distribution dependent on the number~$n$. The paper presents sufficient conditions for the asymptotic normality (for $n\to\infty$…
Moment inequalities play important roles in probability limit theory and mathematical statistics. In this work, the von Bahr-Esseen type inequality for extended negatively dependent random variables under sub-linear expectations is…