Author

V. Ulyanov

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Preprint Oct 2026

Effective-dimension bounds in the central limit theorem for centered Euclidean balls

We establish a nonasymptotic Gaussian approximation bound over centered Euclidean balls for sums of independent, not necessarily identically distributed, random vectors in $\mathbb R^p$. Let $S_n$ denote the sum, let $\Sigma=\operatorname{Var}(S_n)$, and let $G\sim N(0,\Sigma)$. Define the effective rank and th...

A. Naumov, Sergey Samsonov, Vladimir Spokoiny et al. · 0 citations

Aug 2026

Refining the Convergence Rate for $\phi$-Divergence Statistics in Multinomial Goodness-of-Fit Tests

We study asymptotic properties of statistics in goodness-of-fit tests under the simple null hypothesis of a multinomial distribution. It is also assumed that the statistics are based on $\phi$-divergences, the sample size $n$ tends to infinity, and the number of cells in the group $k$ is fixed. It is known that in this...

V. Ulyanov, A. V. Sheryaev · Theory of Probability &... · 0 citations