International audienceWe obtain explicit Berry-Esseen bounds in the Kolmogorov dis- tance for the normal approximation of non-linear functionals of vectors of independent random variables. Our results are based on the use of Stein’s method and of random difference operators, and generalise the bounds obtained by Chatterjee (2008), concerning normal approximations in the Wasserstein distance. In order to obtain lower bounds for variances, we also revisit the classical Hoeffding decompositions, for which we provide a new proof and a new representation. Several applications are discussed in detail: in particular, new Berry-Esseen bounds are obtained for set approximations with random tessellations, as well as for functionals of coverage proces...
Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed (i.i.d.) $d\times d...
Let (Xn) be a sequence of independent identically distributed ran-dom variables with zero means and ...
A Sharpening Of Nonuniform bounds of the Berry-Esseen type initially obtained by Esseen and later ge...
We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstei...
The Stein's method is a collection of probabilistic techniques for answering the ques- tion as to ho...
We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance ...
We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance ...
Peccati, Solè, Taqqu, and Utzet recently combined Stein’s method and Malliavin calculus to obtain a ...
We prove a Berry-Esseen bound in de Jong's classical CLT for normalized, completely degenerate $U$-s...
The classical Berry-Esseen error bound, for the normal approximation to the law of a sum of independ...
We find a sufficient condition for optimal Berry-Esseen bounds in the normal approximation of functi...
The Stein's method is a collection of probabilistic techniques for answering the ques- tion as to ho...
ABSTRACT: Consider sequences {Xi}∞i=1 and {Yj}∞j=1 of independent and identically distributed (i.i.d...
Given a stationary sequence {Xk}kεZ, non-uniform bounds for the normal approximation in the...
Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed (i.i.d.) $d\times d...
Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed (i.i.d.) $d\times d...
Let (Xn) be a sequence of independent identically distributed ran-dom variables with zero means and ...
A Sharpening Of Nonuniform bounds of the Berry-Esseen type initially obtained by Esseen and later ge...
We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstei...
The Stein's method is a collection of probabilistic techniques for answering the ques- tion as to ho...
We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance ...
We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance ...
Peccati, Solè, Taqqu, and Utzet recently combined Stein’s method and Malliavin calculus to obtain a ...
We prove a Berry-Esseen bound in de Jong's classical CLT for normalized, completely degenerate $U$-s...
The classical Berry-Esseen error bound, for the normal approximation to the law of a sum of independ...
We find a sufficient condition for optimal Berry-Esseen bounds in the normal approximation of functi...
The Stein's method is a collection of probabilistic techniques for answering the ques- tion as to ho...
ABSTRACT: Consider sequences {Xi}∞i=1 and {Yj}∞j=1 of independent and identically distributed (i.i.d...
Given a stationary sequence {Xk}kεZ, non-uniform bounds for the normal approximation in the...
Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed (i.i.d.) $d\times d...
Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed (i.i.d.) $d\times d...
Let (Xn) be a sequence of independent identically distributed ran-dom variables with zero means and ...
A Sharpening Of Nonuniform bounds of the Berry-Esseen type initially obtained by Esseen and later ge...
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