Related papers: Two-sided moment estimates for a class of nonnegat…
We obtain quantitative Four Moments Theorems establishing convergence of the laws of elements of a Markov chaos to a Pearson distribution, where the only assumption we make on the Pearson distribution is that it admits four moments. While…
We present order of magnitude estimates for the quantiles of non-negative linear combinations of non-negative random variables, as well as deviation inequalities for general linear combinations of independent random variables, under the…
We extend a general result showing that the asymptotic behavior of high moments, factorial or standard, of random variables, determines the asymptotically normality, from the one dimensional to the multidimensional setting. This approach…
In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…
An unbiased estimator for the ellipticity of an object in a noisy image is given in terms of the image moments. Three assumptions are made: i) the pixel noise is normally distributed, although with arbitrary covariance matrix, ii) the image…
We address the problem of causal effect estimation in the presence of unobserved confounding, but where proxies for the latent confounder(s) are observed. We propose two kernel-based methods for nonlinear causal effect estimation in this…
This paper is focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability,…
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…
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…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
Suppose a sequence of random variables {X_n} has negative drift when above a certain threshold and has increments bounded in L^p. When p>2 this implies that EX_n is bounded above by a constant independent of n and the particular sequence…
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average…
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…
We consider conditional estimation in two-stage sample size adjustable designs and the following bias. More specifically, we consider a design which permits raising the sample size when interim results look rather promising, and, which…
Bounds of the accuracy of the normal approximation to the distribution of a sum of independent random variables are improved under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second.…
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…
We calculate, for a branching random walk $X_n(l)$ to a leaf $l$ at depth $n$ on a binary tree, the positive integer moments of the random variable $\frac{1}{2^{n}}\sum_{l=1}^{2^n}e^{2\beta X_n(l)}$, for $\beta\in\mathbb{R}$. We obtain…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
We establish new conditions for obtaining uniform bounds on the moments of discrete-time stochastic processes. Our results require a weak negative drift criterion along with a state-dependent restriction on the sizes of the one-step jumps…
The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…