Related papers: Moment estimates of Rosenthal type via cumulants
The present paper concentrates on the analogues of Rosenthal's inequalities for ordinary and decoupled bilinear forms in symmetric random variables. More specifically, we prove the exact moment inequalities for these objects in terms of…
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 this paper is to propose new Rosenthal-type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by…
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…
Binomial random intersection graphs can be used as parsimonious statistical models of large and sparse networks, with one parameter for the average degree and another for transitivity, the tendency of neighbours of a node to be connected.…
We discuss a method of the asymptotic computation of moments of the normalized eigenvalue counting measure of random matrices of large order. The method is based on the resolvent identity and on some formulas relating expectations of…
Beginning with work of Zeilberger on classical pattern counts, there are a variety of structural results for moments of permutation statistics applied to random permutations. Using tools from representation theory, Gaetz and Ryba…
Ratios of random variables often appear in probability and statistical applications. We aim to approximate the moments of such ratios under several dependence assumptions. Extending the ideas in Collomb [C. R. Acad. Sci. Paris 285 (1977)…
We derive sharp non - asymptotical Lebesgue - Riesz as well as Grand Lebesgue Space norm estimations for different norms of matrix martingales through these norms for the correspondent martingale differences and through the entropic…
The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. In particular, special attention is paid…
Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to…
This paper proposes a linear categorical random coefficient model, in which the random coefficients follow parametric categorical distributions. The distributional parameters are identified based on a linear recurrence structure of moments…
Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement…
We study the exact constants in the moment inequalities for sums of centered independent random variables: improve their asymptotics, low and upper bounds, calculate more exact asymptotics, elaborate the numerical algorithm for their…
In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical…
Using asymptotics of Toeplitz+Hankel determinants, we establish formulae for the asymptotics of the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices, as the matrix-size tends to infinity.…
The aim of this paper is to give fine asymptotics for random variables with moments of Gamma type. Among the examples we consider are random determinants of Laguerre and Jacobi beta ensembles with varying dimensions (the number of observed…
The problem of convergence of moments of a sequence of random variables to the moments of its asymptotic distribution is important in many applications. These include the determination of the optimal training sample size in the cross…
We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only low orders. Our bounds depend on the ``intrinsic''…
In this paper relations among some kinds of cumulative entropies and moments of order statistics are presented. By using some characterizations and the symmetry of a non negative and absolutely continuous random variable X, lower and upper…