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

Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…

We consider a random model for directed graphs whereby an arc is placed from one vertex to another with a prescribed probability which may vary from arc to arc. Using perturbation bounds as well as Chernoff inequalities, we show that the…

We consider smooth linear statistics of determinantal point processes on the complex plane, and their large scale asymptotics. We prove asymptotic normality in the finite variance case, where Soshnikov's theorem is not applicable. The…

A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…

Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the Strong Law of Large Numbers for (symmetrized) U-statistics. We also obtain nasc's for the a.s. convergence of series of an…

The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in…

Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to…

In the common time series model $X_{i,n} = \mu (i/n) + \varepsilon_{i,n}$ with non-stationary errors we consider the problem of detecting a significant deviation of the mean function $\mu$ from a benchmark $g (\mu )$ (such as the initial…

One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are universal. We probe the edges of universality by studying the spectral properties of random…

We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…

In this paper, we consider approximating expansions for the distribution of integer valued random variables, in circumstances in which convergence in law cannot be expected. The setting is one in which the simplest approximation to the…

We derive asymptotic normality of kernel type deconvolution estimators of the density, the distribution function at a fixed point, and of the probability of an interval. We consider the so called super smooth case where the characteristic…

We show that the stationary distribution of a finite Markov chain can be expressed as the sum of certain normal distributions. These normal distributions are associated to planar graphs consisting of a straight line with attached loops. The…

In 2016, Karney proposed an exact sampling algorithm for the standard normal distribution. In this paper, we study the computational complexity of this algorithm under the random deviate model. Specifically, Karney's algorithm requires the…

We propose a modified density estimation problem that is highly effective for detecting anomalies in tabular data. Our approach assumes that the density function is relatively stable (with lower variance) around normal samples. We have…

In this paper, we consider semi-Markov processes whose transition times and transition probabilities depend on a small parameter $\varepsilon$. Understanding the asymptotic behavior of such processes is needed in order to study the…

We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…

Testing for normality is a widely used procedure in statistics and data analysis, often applied prior to employing methods that rely on the assumption of normally distributed data. While several existing tests target distributional…

Consider a Gaussian stationary sequence with unit variance $X=\{X_k;k\in {\mathbb{N}}\cup\{0\}\}$. Assume that the central limit theorem holds for a weighted sum of the form $V_n=n^{-1/2}\sum^{n-1}_{k=0}f(X_k)$, where $f$ designates a…

We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini's mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic,…