相关论文: Estimates for the strong approximation in multidim…
We present several refinements on the fluctuations of sequences of random vectors (with values in the Euclidean space $\mathbb{R}^d$) which converge after normalization to a multidimensional Gaussian distribution. More precisely we refine…
We obtain an optimal bound for a Gaussian approximation of a large class of vector-valued random processes. Our results provide a substantial generalization of earlier results that assume independence and/or stationarity. Based on the decay…
We obtain almost sure limit theorems for partial maxima of norms of a sequence of Banach-valued Gaussian random variables.
We establish the rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution in terms of truncated pseudomoments by implementing the idea of Yu. Studnyev for getting…
We establish generalized Gaussian bounds and local limit theorems with Gaussian-type error for the convolution powers of certain complex-valued functions on $\mathbb{Z}^d$. These global space-times estimates/error, which are sharp in…
The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…
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…
We establish optimal logarithmic rates of convergence in the strong invariance principle for multivariate cumulative processes in the Smith's sense. Exponential probabilistic inequalities of Koml\'{o}s-Major-Tusn\'{a}dy type are obtained.…
We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by infinitely divisible laws may be transferred to the estimation of the closeness of…
Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…
Most of the modern literature on robust mean estimation focuses on designing estimators which obtain optimal sub-Gaussian concentration bounds under minimal moment assumptions and sometimes also assuming contamination. This work looks at…
In this paper we give anticoncentration bounds for sums of independent random vectors in finite-dimensional vector spaces. In particular, we asymptotically establish a conjecture of Leader and Radcliffe (1994) and a question of Jones…
The "typical" asymptotic behavior of the weighted sums of independent, identically distibuted random vectors in k-dimensional space is considered. It is shown that under finitnes of fifth absolute moment of an individual term the rate of…
Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. The paper deals with the question about the behavior of the concentration function of the random variable $\sum\limits_{k=1}^{n}X_k a_k$ according to the…
Nearest neighbor cells in $R^d,d\in\mathbb{N}$, are used to define coefficients of divergence ($\phi$-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a…
The celebrated results of Koml\'os, Major and Tusn\'ady [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] give optimal Wiener approximation for the partial sums of i.i.d. random variables and provide a…
The Bonferroni adjustment, or the union bound, is commonly used to study rate optimality properties of statistical methods in high-dimensional problems. However, in practice, the Bonferroni adjustment is overly conservative. The extreme…
We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…
We study the central limit theorem for sums of independent tensor powers, $\frac{1}{\sqrt{d}}\sum\limits_{i=1}^d X_i^{\otimes p}$. We focus on the high-dimensional regime where $X_i \in \mathbb{R}^n$ and $n$ may scale with $d$. Our main…