Estimates of stability with respect to the number of summands for distributions of successive sums of independent identically distributed vectors

Autor: Zaitsev, Andrei Yu.

Publikováno v: Zapiski Nauchnykh Seminarov POMI, 2023, v.525, 86-95 (in Russian)

Let $X_1,\dots, X_n,\dots$ be i.i.d.\ $d$-dimensional random vectors with common distribution $F$. Then $S_n = X_1+\dots+X_n$ has distribution $F^n$ (degree is understood in the sense of convolution). Let $$ \rho_{\mathcal{C}_d}(F,G) = \sup_A |F\{A\}

Externí odkaz: http://arxiv.org/abs/2310.20283

A new bound in the Littlewood--Offord problem

Autor: Götze, Friedrich, Zaitsev, Andrei Yu.

Publikováno v: Mathematics, 2022, 10(10), 1740

The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions.
Comment: 7 pages. arXiv admin note: substantial text overlap with arXi

Externí odkaz: http://arxiv.org/abs/2112.12574

On alternative approximating distributions in the multivariate version of Kolmogorov's second uniform limit theorem

Autor: Götze, Friedrich, Zaitsev, Andrei Yu.

Publikováno v: Theory Probab. Appl., v. 62, no.1 (2022), 3-22 (in Russian); English translation Theory Probab. Appl. 67, No. 1, 1-16 (2022)

The aim of the present work is to show that recent results of the authors on the approximation of distributions of sums of independent summands by the infinitely divisible laws on convex polyhedra can be shown via an alternative class of approximatin

Externí odkaz: http://arxiv.org/abs/2006.01942

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Moderate deviations for the $L_1$-norm of kernel density estimators

Autor: Zaitsev, Andrei Yu.

Publikováno v: Vestnik St. Petersburg University: Mathematics 2005, no. 4, 21-33 (in Russian); English translation in: Vestnik St. Petersburg University: Mathematics, 38:4 (2005), 15-24

The rate of normal approximation for the integral norm of kernel density estimators is investigated in the case of densities with power-type singularities. The quantities from the formulations of published results by the author are estimated. By assu

Externí odkaz: http://arxiv.org/abs/1805.01770