Related papers: Strong Gaussian approximations with random multipl…
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…
We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the…
We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$,…
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
In a recent paper the author obtained optimal bounds for the strong Gaussian approximation of sums of independent $\R^d$-valued random vectors with finite exponential moments. The results may be considered as generalizations of well-known…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
Under certain mild conditions, limit theorems for additive functionals of some $d$-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions,…
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…
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 central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…
In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
Motivated by the Central Limit Theorem, in this paper, we study both universal and non-universal simulations of random variables with an arbitrary target distribution $Q_{Y}$ by general mappings, not limited to linear ones (as in the…
We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…