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Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…

Methodology · Statistics 2024-04-23 Jiazhen Xu , Janice L. Scealy , Andrew T. A. Wood , Tao Zou

In this paper we derive inferential results for a new index of inequality, specifically defined for capturing significant changes observed both in the left and in the right tail of the income distributions. The latter shifts are an apparent…

Statistics Theory · Mathematics 2017-06-20 Youri Davydov , Francesca Greselin

Inverse statistics in economics is considered. We argue that the natural candidate for such statistics is the investment horizons distribution. This distribution of waiting times needed to achieve a predefined level of return is obtained…

Soft Condensed Matter · Physics 2008-12-02 Mogens H. Jensen , Anders Johansen , Ingve Simonsen

This article focuses on some properties of three tools used to measure economic inequalities with respect to a distribution of wealth $\mu$: Gini coefficient $G$, Hoover coefficient or Robin Hood coefficient $H$, and the Lorenz…

Probability · Mathematics 2024-10-22 Valentin Melot

We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message…

Information Theory · Computer Science 2012-08-15 Sundeep Rangan

We consider the invariant measure of a homogeneous continuous- time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be…

Probability · Mathematics 2014-02-25 Yanting Chen , Richard J. Boucherie , Jasper Goseling

A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral norm of general Gaussian random matrices $X=\sum_i g_i A_i$ where $g_i$ are independent…

Probability · Mathematics 2023-09-18 Afonso S. Bandeira , March T. Boedihardjo , Ramon van Handel

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among…

Methodology · Statistics 2022-07-11 Tsubasa Ito , Shonosuke Sugasawa

We examine the optimality properties of the Gini index estimator under complex survey design involving stratification, clustering, and sub-stratification. While Darku et al. (Econometrics, 26, 2020) considered only stratification and…

Methodology · Statistics 2026-02-26 Shivam , Bhargab Chattopadhyay , Nil Kamal Hazra

The maximum a-posteriori (MAP) perturbation framework has emerged as a useful approach for inference and learning in high dimensional complex models. By maximizing a randomly perturbed potential function, MAP perturbations generate unbiased…

Machine Learning · Computer Science 2013-10-17 Francesco Orabona , Tamir Hazan , Anand D. Sarwate , Tommi Jaakkola

We introduce the first analytical model of asymmetric community dynamics to yield Hubbell's neutral theory in the limit of functional equivalence among all species. Our focus centers on an asymmetric extension of Hubbell's local community…

Populations and Evolution · Quantitative Biology 2010-12-06 Andrew E. Noble , Nico M. Temme , William F. Fagan , Timothy H. Keitt

In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…

Mathematical Physics · Physics 2024-03-26 Grégoire Sergeant-Perthuis

In this paper we will show that the Gini coefficient and the introduced measure of angular inequality are special cases of a wider indexed family of measurements. We will discuss the properties of the defined class based, inter alia, on a…

Methodology · Statistics 2015-06-02 Piotr Dniestrzanski

It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov's theorem, we further investigate the analogous characteristic properties in terms of the sample mean…

Statistics Theory · Mathematics 2021-12-14 Chin-Yuan Hu , Gwo Dong Lin

We study properties of the harmonic measure of balls in large critical Galton-Watson trees whose offspring distribution is in the domain of attraction of a stable distribution with index $\alpha\in (1,2]$. Here the harmonic measure refers…

Probability · Mathematics 2014-05-08 Shen Lin

We propose a testing and estimation methodology for univariate and bivariate symmatric $\alpha$-stable distributions using a modified version of the Greenwood statistic. Originally designed for positive-valued random variables, the…

The ability to quantify distinctness of a cluster structure is fundamental for certain simulation studies, in particular for those comparing performance of different classification algorithms. The intrinsic integral measure based on the…

Statistics Theory · Mathematics 2014-07-29 Ewa Nowakowska , Jacek Koronacki , Stan Lipovetsky

We study the problem of estimating the common mean $\mu$ of $n$ independent symmetric random variables with different and unknown standard deviations $\sigma_1 \le \sigma_2 \le \cdots \le\sigma_n$. We show that, under some mild regularity…

Statistics Theory · Mathematics 2020-10-23 Luc Devroye , Silvio Lattanzi , Gabor Lugosi , Nikita Zhivotovskiy

In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in…

Machine Learning · Statistics 2022-03-18 Xiao-Tong Yuan , Ping Li

We investigate the repeated averaging model for money exchanges: two agents picked uniformly at random share half of their wealth to each other. It is intuitively convincing that a Dirac distribution of wealth (centered at the initial…

Probability · Mathematics 2021-08-19 Fei Cao