Related papers: Moment estimates of Rosenthal type via cumulants
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the…
For the multivariate COGARCH process, we obtain explicit expressions for the second-order structure of the "squared returns" process observed on an equidistant grid. Based on this, we present a generalized method of moments estimator for…
We establish a new connection between moments of $n \times n$ random matrices $X_n$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\mathbb{E}\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s \in…
We give a new proof of correlation estimates for arbitrary moments of the resolvent of random Schr\"odinger operators on the lattice that generalizes and extends the correlation estimate of Minami for the second moment. We apply this moment…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
We consider an ensemble of nxn real symmetric random matrices A whose entries are determined by independent identically distributed random variables that have symmetric probability distribution. Assuming that the moment 12+2delta of these…
We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…
Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the…
In this article, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the estimated conditional…
This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of…
We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the…
Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled…
Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
We investigate the convergence of series of random variables with second exponential moments. We give sufficient conditions for the convergence of these series with respect to an exponential Orlicz norm and almost surely. Applying this…
Let $X_1, \ldots, X_n\in\mathbb{R}^p$ be i.i.d. random vectors. We aim to perform simultaneous inference for the mean vector $\mathbb{E} (X_i)$ with finite polynomial moments and an ultra high dimension. Our approach is based on the…
We give an asymptotic formula for the $2k$th moment of a sum of multiplicative Steinhaus variables. This was recently computed independently by Harper, Nikeghbali and Radziwi\l\l. We also compute the $2k$th moment of a truncated…
The theory of rapid mixing random walks plays a fundamental role in the study of modern randomised algorithms. Usually, the mixing time is measured with respect to the worst initial position. It is well known that the presence of…
As a former engineering student, I have a great interest in a real world application of mathematics. Probability is something I can relate to. I am lucky enough that after I switched to Mathematics, this is one of many interests of my Ph.D.…