Related papers: Method of Moments Histograms
The problem of the estimation of relevance to a set of histograms generated by samples of a discrete time process is discussed on the base of the variational principles proposed in the previous paper [1]. Some conditions for dimension…
Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…
We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration…
The conformal flow of metrics [2] has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the…
We propose a hybrid moment method for the multi-scale kinetic equations in the framework of the regularized moment method [7]. In this method, the fourth order moment system is chosen as the governing equations in the fluid region. When…
It is shown that all the Frequentist methods are equivalent from a statistical point of view, but the physical significance of the confidence intervals depends on the method. The Bayesian Ordering method is presented and confronted with the…
We retrieve depth information (moments) of an object using partially coherent fields and defocus induced holographic contrast. Our analysis leads to a form of tomography that does not require sample or source rotation. The tomography method…
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…
In this study, we propose a general model capable of addressing heterogeneity in higher-order moments while preserving mean and variance, including the t, Laplace, and skew-normal distributions as special cases. Our model flexibly…
Our goal is to obtain a complete set of angular observables arising in a generic multi-body process. We show how this can be achieved without the need to carry out a likelihood fit of the angular distribution to the measured events.…
Let $\mathsf{A}=\{a_1,\dots,a_m\}$, $m\in\mathbb{N}$, be measurable functions on a measurable space $(\mathcal{X},\mathfrak{A})$. If $\mu$ is a positive measure on $(\mathcal{X},\mathfrak{A})$ such that $\int a_i d\mu<\infty$ for all $i$,…
This paper proposes a semidefinite programming based method for estimating moments of a stochastic hybrid system (SHS). For polynomial SHSs -- which consist of polynomial continuous vector fields, reset maps, and transition intensities --…
One of the reasons that higher order moment portfolio optimization methods are not fully used by practitioners in investment decisions is the complexity that these higher moments create by making the optimization problem nonconvex. Many few…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
We introduce a novel method for obtaining a wide variety of moments of any random variable with a well-defined moment-generating function (MGF). We derive new expressions for fractional moments and fractional absolute moments, both central…
We propose skewed stable random projections for approximating the pth frequency moments of dynamic data streams (0<p<=2), which has been frequently studied in theoretical computer science and database communities. Our method significantly…
The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…
In this paper a new method of experimental data analysis, the Particle-Set Identification method, is presented. The method allows to reconstruct moments of multiplicity distribution of identified particles. The difficulty the method copes…
Generalized empirical likelihood and generalized method of moments are well spread methods of resolution of inverse problems in econometrics. Each method defines a specific semiparametric model for which it is possible to calculate…
We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.