8 citations · 44 across the 12 of their papers we have counts for
15 papers
Effective-dimension bounds in the central limit theorem for centered Euclidean balls
Alexey Naumov, Sergey Samsonov, Vladimir Spokoiny +1
We establish a nonasymptotic Gaussian approximation bound over centered Euclidean balls for sums of independent, not necessarily identically distributed, random vectors in \(\mathb…
From classical to modern central limit theorems
Vladimir V. Ulyanov
De Moivre (1733), investigating the limit distribution of the binomial distribution, was the first to discover the existence of the normal distribution and the central limit theore…
Approximation of Sums of Locally Dependent Random Variables via Perturbation of Stein Operator
Zhonggen Su, Vladimir V. Ulyanov, Xiaolin Wang
Let be a family of locally dependent nonnegative integer-valued random variables, and consider the sum . We first establish a general…
On De la Peña Type Inequalities for Point Processes
Naiqi Liu, Vladimir V. Ulyanov, Hanchao Wang
There has been a renewed interest in exponential concentration inequalities for stochastic processes in probability and statistics over the last three decades. De la Peña \cite{d}…
A multivariate CLT for <<typical>> weighted sums with rate of convergence of order O(1/n)
Sagak A. Ayvazyan, Vladimir V. Ulyanov
The "typical" asymptotic behavior of the weighted sums of independent random vectors in -dimensional space is considered. It is shown that in this case the rate of convergence i…
Inference via Randomized Test Statistics
Nikita Puchkin, Vladimir Ulyanov
We show that external randomization may enforce the convergence of test statistics to their limiting distributions in particular cases. This results in a sharper inference. Our app…
On rate of convergence to the Poisson law of the number of cycles in the generalized random graphs
Sergey G. Bobkov, Maria A. Danshina, Vladimir V. Ulyanov
Convergence of order is obtained for the distance in total variation between the Poisson distribution and the distribution of the number of fixed size cycles in gen…
Two-sided inequalities for the density function's maximum of weighted sum of chi-square variables
Sergey G. Bobkov, Alexey A. Naumov, Vladimir V. Ulyanov
Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are consi…
Second Order Expansions for Sample Median with Random Sample Size
Gerd Christoph, Vladimir V. Ulyanov, Vladimir E. Bening
In practice, we often encounter situations where a sample size is not defined in advance and can be a random value. The randomness of the sample size crucially changes the asymptot…
Large ball probability, Gaussian comparison and anti-concentration
Friedrich Götze, Alexey Naumov, Vladimir Spokoiny +1
We derive tight non-asymptotic bounds for the Kolmogorov distance between the probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bou…
Bootstrap confidence sets for spectral projectors of sample covariance
Alexey Naumov, Vladimir Spokoiny, Vladimir Ulyanov
Let be i.i.d. sample in with zero mean and the covariance matrix . The problem of recovering the projector onto an eigenspace of $\m…
On Properties of Polynomials in Random Elements
Vladimir V. Ulyanov
The paper deals with different properties of polynomials in random elements: bounds for characteristics functionals of polynomials, stochastic generalization of the Vinogradov mean…
Non-asymptotic results for Cornish--Fisher expansions
V. V. Ulyanov, M. Aoshima, Y. Fujikoshi
We get the computable error bounds for generalized Cornish-Fisher expansions for quantiles of statistics provided that the computable error bounds for Edgeworth-Chebyshev type expa…
Tunnelling series in terms of perturbation theory for quantum spin systems
V. V. Ulyanov, O. B. Zaslavskii
Considered is quantum tunnelling in anisotropic spin systems in a magnetic field perpendicular to the anisotropy axis. In the domain of small field the problem of calculating tunne…
Spin systems, spin coherent states and quasi-exactly solvable models
V. V. Ulyanov, O. B. Zaslavskii
Spin coherent states play a crucial role in defining QESM (quasi-exactly solvable models) establishing a strict correspondence between energy spectra of spin systems and low-lying…