Related papers: The optimal fourth moment theorem
We investigate the multivariate central limit theorem for nonlinear statistics by means of Stein's method and Slepian's smart path interpolation method. Based on certain difference operators in theory of concentration inequalities, we…
We consider stochastic optimization problems with the dual tasks of (i) effectively finding the optimizer and (ii) reliably conducting statistical inference for the optimal objective function value. We find that classical simulation…
We prove a quantitative Fourth Moment Theorem for Wigner integrals of any order with symmetric kernels, generalizing an earlier result from Kemp et al. (2012). The proof relies on free stochastic analysis and uses a new biproduct formula…
We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of…
We investigate the optimal rate of convergence in the multidimensional normal approximation of vector-valued Wiener-Ito integrals of which components all belong to the same fixed Wiener chaos. Combining Malliavin calculus, Stein's method…
We prove Berry-Esseen type rates of convergence for central limit theorems (CLTs) of regenerative processes which generalize previous results of Bolthausen under weaker moment assumptions. We then show how this general result can be applied…
By combining the findings of two recent, seminal papers by Nualart, Peccati and Tudor, we get that the convergence in law of any sequence of vector-valued multiple integrals $F_n$ towards a centered Gaussian random vector $N$, with given…
We study linear spectral statistics of high dimensional sample covariance matrices in a regime where the empirical spectral distribution remains governed by the classical sample covariance law but the fluctuation theory is nonclassical. Our…
In this paper, we study second order fluctuations for the size of the range of a critical branching random walk (BRW) in $\mathbb Z^d$. We consider the BRW with geometric offspring indexed by the Kesten tree, and show that the size of its…
In [NP09a], Nourdin and Peccati established a neat characterization of Gamma approximation on a fixed Wiener chaos in terms of convergence of only the third and fourth cumulants. In this paper, we investigate the rate of convergence in…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
We investigate the probability density of rescaled sums of iterates of deterministic dynamical systems, a problem relevant for many complex physical systems consisting of dependent random variables. A Central Limit Theorem (CLT) is only…
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.
The leading term in the normal approximation to the distribution of Student's t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form…
We show that a necessary and sufficient condition for the sum of iid random vectors to converge (under appropriate shifting and scaling) to a multivariate Gaussian distribution is that the truncated second moment matrix is slowly varying at…
The purpose of the present paper is to establish moment estimates of Rosenthal type for a rather general class of random variables satisfying certain bounds on the cumulants. We consider sequences of random variables which satisfy a central…
We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \varepsilon_{n}(f):={\mathbb{E}}\Big(f\Big(\frac 1{\sqrt…
We investigate the problem of finding necessary and sufficient conditions for convergence in distribution towards a general finite linear combination of independent chi-squared random variables, within the framework of random objects living…
Consider $F$ an element of the second Wiener chaos with variance one. In full generality, we show that, for every integer $p\ge 1$, there exists $\eta_p>0$ such that if $\kappa_4(F)<\eta_p$ then the Malliavin derivative of $F$ admits a…