Related papers: Asymptotic Results for the Two-parameter Poisson-D…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
We consider several sequences of random variables whose Fourier-Laplace transforms present the same type of \textit{splitting phenomenon} when suitably rescaled by the Fourier-Laplace transform of a Poisson-distributed random variable…
The possibility of construction of continuous analogue of Poisson distribution with the search of bounds of confidence intervals for parameter of Poisson distribution is discussed. Also, in the article is shown that the true value of a…
Consider the random quadratic form $T_n=\sum_{1 \leq u < v \leq n} a_{uv} X_u X_v$, where $((a_{uv}))_{1 \leq u, v \leq n}$ is a $\{0, 1\}$-valued symmetric matrix with zeros on the diagonal, and $X_1,$ $X_2, \ldots, X_n$ are i.i.d.…
In the present paper, we consider the Pearson chi-square statistic defined on a finite alphabet which is assumed to dynamically vary as the sample size increases, and establish its moderate deviation principle.
Distribution of the sum of independent identically distributed symmetric lattice vectors is approximated by the accompanying compound Poisson law and the second-order Hipp-type signed compound Poisson measure. Bergstr\"om -type asymptotic…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We give a simple inequality that compares the laws of two random variables taking values in a convex subset of a normed vector space. By combining this with Arratia's coupling, recently refined by Koukoulopoulos and the author, we obtain a…
Bounds of the accuracy of the normal approximation to the distribution of a sum of independent random variables are improved under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second.…
The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for some planary random…
Let $X$ have a Generalized Poisson distribution with mean $kb$, where $b$ is a known constant in the unit interval and $k$ is a discrete, non-negative parameter. We show that if an uninformative uniform prior for $k$ is assumed, then the…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
The two-dimensional one-component plasma is an ubiquitous model for several vortex systems. For special values of the coupling constant $\beta q^2$ (where $q$ is the particles charge and $\beta$ the inverse temperature), the model also…
Asymptotic distribution for the proportional covariance model under multivariate normal distributions is derived. To this end, the parametrization of the common covariance matrix by its Cholesky root is adopted. The derivations are made in…
We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…
A random phenomenon may have two sources of random variation: an unstable identity and a set of external variation-generating factors. When only a single source is active, two mutually exclusive extreme scenarios may ensue that result in…
A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that are equi-dispersed constitutes…