Related papers: A note on the permutation distribution of generali…
Gibbs random fields play an important role in statistics, however, the resulting likelihood is typically unavailable due to an intractable normalizing constant. Composite likelihoods offer a principled means to construct useful…
We use new bounds of double exponential sums with ratios of integers from prescribed intervals to get an asymptotic formula for the number of solutions to congruences $$ \sum_{j=1}^n a_j x_jy_j^{-1} \equiv a_0 \pmod p, $$ with variables…
In this paper, we establish uniform asymptotic certainty bands for the conditional cumulative distribution function. To this aim, we give exact rate of strong uniform consistency for the local linear estimator of this function. The…
We introduce the notion of a weighted inversion statistic on the symmetric group, and examine its distribution on each conjugacy class. Our work generalizes the study of several common permutation statistics, including the number of…
The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…
For an array $\left\{X_{n,j}, \, 1 \leqslant j \leqslant k_{n}, n \geqslant 1 \right\}$ of random variables and a sequence $\{c_{n} \}$ of positive numbers, sufficient conditions are given under which, for all $\varepsilon > 0$,…
We adapt the techniques in Stigler [Ann. Statist. 1 (1973) 472--477] to obtain a new, general asymptotic result for trimmed $U$-statistics via the generalized $L$-statistic representation introduced by Serfling [Ann. Statist. 12 (1984)…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
In this work, we show that Spearman's correlation coefficient test about $H_0:\rho_s=0$ found in most statistical software packages is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the…
We consider the problem of calculating distance correlation coefficients between random vectors whose joint distributions belong to the class of Lancaster distributions. We derive under mild convergence conditions a general series…
Simple sufficient conditions are given that ensure the uniform continuity in distribution for Borel transformations of random fields.
We present progress in the QCD analysis of the Bjorken sum rule at low momentum transfers. We study asymptotic structure of the perturbative QCD expansion at low $Q^2$ scales based on analysis of recent accurate data on the Bjorken sum rule…
Using the recently discovered strong negative dependence properties of the symmetric exclusion process, we derive general conditions for when the normalized current of particles between regions converges to the Gaussian distribution. The…
We study asymptotic infinitesimal distributions of Gaussian Unitary Ensembles with permuted entries. We show that for random uniform permutations, the asymptotically permuted GUE matrix has a null infinitesimal distribution. Moreover, we…
A weighted U-statistic based on a random sample X_1,...,X_n has the form U_n=\sum_{1\le i,j\le n}w_{i-j}K(X_i,X_j), where K is a fixed symmetric measurable function and the w_i are symmetric weights. A large class of statistics can be…
We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…
In this paper, the uniformly asymptotic normality for sample quantiles of associated random variables is investigated under some conditions on the decay of the covariances. We obtain the rate of normal approximation of order…
We study the asymptotic distribution of zeros for the random polynomials $P_n(z) = \sum_{k=0}^n A_k B_k(z)$, where $\{A_k\}_{k=0}^{\infty}$ are non-trivial i.i.d. complex random variables. Polynomials $\{B_k\}_{k=0}^{\infty}$ are…
Generalized Jacobi polynomials are orthogonal polynomials related to a weight function which is smooth and positive on the whole interval of orthogonality up to a finite number of points, where algebraic singularities occur. The influence…
In this article we give a purely noncommutative criterion for the characterization of two-state normal distribution. We prove that families of two-state normal distribution can be described by relations which is similar to the conditional…