Related papers: Normal Approximation for $U$- and $V$-statistics o…

The number of comparisons X_n used by Quicksort to sort an array of n distinct numbers has mean mu_n of order n log n and standard deviation of order n. Using different methods, Regnier and Roesler each showed that the normalized variate…

The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular…

We give the asymptotic behavior of the Mann-Whitney U-statistic for two independent stationary sequences. The result applies to a large class of short-range dependent sequences, including many non-mixing processes in the sense of…

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…

We investigate the asymptotic behavior of several variants of the scan statistic applied to empirical distributions, which can be applied to detect the presence of an anomalous interval with any length. Of particular interest is Studentized…

We establish large deviation formulas for linear statistics on the $N$ transmission eigenvalues $\{T_i\}$ of a chaotic cavity, in the framework of Random Matrix Theory. Given any linear statistics of interest $A=\sum_{i=1}^N a(T_i)$, the…

We establish the rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution in terms of truncated pseudomoments by implementing the idea of Yu. Studnyev for getting…

Sequential probability assignment and universal compression go hand in hand. We propose sequential probability assignment for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded…

In this paper, we investigated the effect on extreme of random replacing for a stationary sequence satisfying a type of long dependent condition and a local dependent condition, and derived the joint asymptotic distribution of maximum from…

This paper derives the rate of convergence and asymptotic distribution for a class of Kolmogorov-Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general…

Let $X_0$ be a non-constant random variable with finite variance. Given an integer $k\ge2$, define a sequence $\{X_n\}_{n=1}^\infty$ of approximately linear recursions with small perturbations $\{\Delta_n\}_{n=0}^\infty$ by $$X_{n+1} =…

We study the effect of observing a stationary process at irregular time points via a renewal process. We establish a sharp difference in the asymptotic behaviour of the self-normalized sample mean of the observed process depending on the…

Let $X_{1},X_{2},...$ be a sequence of independent copies (s.i.c) of a real random variable (r.v.) $X\geq 1$, with distribution function $df$ $F(x)=\mathbb{P}% (X\leq x)$ and let $X_{1,n}\leq X_{2,n} \leq ... \leq X_{n,n}$ be the order…

We study stationary distributions in the context of stochastic reaction networks. In particular, we are interested in complex balanced reaction networks and reduction of such networks by assuming a set of species (called non-interacting…

We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…

We prove a general transfer theorem for multivariate random sequences with independent random indexes in the double array limit setting. We also prove its partial inverse providing necessary and sufficient conditions for the convergence of…

In a recent paper by the authors, a new approach--called the "embedding method"--was introduced, which allows to make use of exchangeable pairs for normal and multivariate normal approximation with Stein's method in cases where the…

We consider the modulation of data given by random vectors $X_n \in \mathbb{R}^{d_n}$, $n \in \mathbb{N}$. For each $X_n$, one chooses an independent modulating random vector $\Xi_n \in \mathbb{R}^{d_n}$ and forms the projection $Y_n =…

Let $E$ be a space of observables in a sequence of trials $\xi_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $\psi$-weak topology of…

A characterization of the exponential distribution based on equidistribution conditions for maxima of random samples with consecutive sizes n-1 and n for an arbitrary and fixed n>2 is proved. This solves an open problem stated recently in…