Related papers: Concentration of normalized sums and a central lim…

In a paper that appeared in 2010, C. Tone proved a multivariate central limit theorem for some strictly stationary random fields of random vectors satisfying certain mixing conditions. The "normalization" of a given "partial sum" (or "block…

Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…

The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…

We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit…

Regarding the conjugacy representation on symmetric groups, we initiate a normalized measure emerging from this representation, namely the conjugacy measure. A central limit theorem for character ratios of random representations of the…

In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.

The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincar\'{e}-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical…

A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…

We prove a central limit theorem for random sums of the form $\sum_{i=1}^{N_n} X_i$, where $\{X_i\}_{i \geq 1}$ is a stationary $m-$dependent process and $N_n$ is a random index independent of $\{X_i\}_{i\geq 1}$. Our proof is a…

Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on these return times. This result has applications to entropy…

The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…

In this article we introduce associative Look-Up Tables. With their help, pseudo sums are correctly determined. The set of limit distributions in a pseudo-summation scheme of i.i.d. random variables is described. Also, two special cases…

We consider the self-normalized sums $T_{n}=\sum_{i=1}^{n}X_{i}Y_{i}/\sum_{i=1}^{n}Y_{i}$, where ${Y_{i} : i\geq 1}$ are non-negative i.i.d. random variables, and ${X_{i} : i\geq 1} $ are i.i.d. random variables, independent of ${Y_{i} : i…

The limit behavior is studied for the distributions of normalized U- and V-statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying…

We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein…

We explore the applications of our previously established likelihood-ratio method for deriving concentration inequalities for a wide variety of univariate and multivariate distributions. New concentration inequalities for various…

Using a renormalization approach, we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power q(n) that varies monotonically with the sample size n.…

We propose a general scheme to create time sequences that fulfill given constraints but are random otherwise. Significance levels for nonlinearity tests are as usually obtained by Monte Carlo resampling. In a new scheme, constraints…

The paper that is commented by Touchette contains a computational study which opens the door to a desirable generalization of the standard large deviation theory (applicable to a set of $N$ nearly independent random variables) to systems…

The general model of coagulation is considered. For basic classes of unbounded coagulation kernels the central limit theorem (CLT) is obtained for the fluctuations around the dynamic law of large numbers (LLN). A rather precise rate of…