相关论文: Numerically Stable Evaluation of Moments of Random…
This paper addresses the development of analytical tools for the computation of the moments of random Gram matrices with one side correlation. Such a question is mainly driven by applications in signal processing and wireless communications…
Spectral properties of Gram matrices are central to high dimensional asymptotic analyses of statistical estimators in regression and covariance estimation. These properties, in turn, depend critically on the extreme singular values and…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for…
The non-equilibrium steady states emerging from stochastic resetting to a distribution is studied. We show that for a range of processes, the steady-state moments can be expressed as a linear combination of the moments of the distribution…
In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical…
In the present work, an approach to the moment closure problem on the basis of orthogonal polynomials derived from Gram matrices is proposed. Its properties are studied in the context of the moment closure problem arising in gas kinetic…
In this paper, we propose a method based on GMM (the generalized method of moments) to estimate the parameters of stable distributions with $0<\alpha<2$. We don't assume symmetry for stable distributions.
We obtain new closed-form formulas for the moments and absolute moments of the variance-gamma distribution. We thus deduce new formulas for the moments and absolute moments of the product of two correlated zero mean normal random variables.
Following the student t-statistic, normalization has been a widely used method in statistic and other disciplines including economics, ecology and machine learning. We focus on statistics taking the form of a ratio over (some power of) the…
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…
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…
Model-based prediction of stochastic noise in biomolecular reactions often resorts to approximation with unknown precision. As a result, unexpected stochastic fluctuation causes a headache for the designers of biomolecular circuits. This…
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…
Several applications of the moment method in random matrix theory, especially, to local eigenvalue statistics at the spectral edges, are surveyed, with emphasis on a modification of the method involving orthogonal polynomials.
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…
Trigonometric formulas for eigenvalues of $3 \times 3$ matrices that build on Cardano's and Vi\`ete's work on algebraic solutions of the cubic are numerically unstable for matrices with repeated eigenvalues. This work presents numerically…
We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices : any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the…
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…
We describe an elementary method to get non-asymptotic estimates for the moments of Hermitian random matrices whose elements are Gaussian independent random variables. As the basic example, we consider the GUE matrices. Immediate…