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Understanding rare events is critical across domains ranging from signal processing to reliability and structural safety, extreme-weather forecasting, and insurance. The analysis of rare events is a computationally challenging problem,…

This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the…

Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…

Bobkov (J. Theoret. Probab. 18(2) (2005) 399-412) investigated an approximate de Finetti representation for probability measures, on product measurable spaces, which are symmetric under permutations of coordinates. One of the main results…

We consider a type of nonnormal approximation of infinitely divisible distributions that incorporates compound Poisson, Gamma, and normal distributions. The approximation relies on achieving higher orders of cumulant matching, to obtain…

The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general random matrices in terms of an associated noncommutative model. These…

The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress…

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

Systems of orthogonal polynomials whose recurrence coefficients tend to infinity are considered. A summability condition is imposed on the coefficients and the consequences for the measure of orthogonality are discussed. Also discussed are…

We estimate the number of integer solutions to decomposable form inequalities (both asymptotic estimates and upper bounds are provided) when the degree of the form and the number of variables are relatively prime. These estimates display…

We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…

We propose and analyze a specific asymptotic stochastic order for random processes based on the measure of departure discussed in the literature. As applications, we stochastically compare mixtures of order statistics and record values…

Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…

We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…

We consider the joint density distribution of the elements of certain random matrix models which are example of globally correlated and asymptotically scale-invariant distributions. It is shown that in their cases, the nonadditive entropy…

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…

We establish a large deviation principle for the empirical spectral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo's result for Wigner matrices having the same type of entries [7]. To…

We prove the first generalization bound for large-margin halfspaces that is asymptotically tight in the tradeoff between the margin, the fraction of training points with the given margin, the failure probability and the number of training…

We construct a non - improved exponential bounds for distribution of normed sums of i.,i.d. random variables with random numbers of summand.

Asymptotics are given for the number of rational points in the domain of a morphism of weighted projective stacks whose images have bounded height and satisfy a (possibly infinite) set of local conditions. As a consequence we obtain results…