Related papers: Gini estimation under infinite variance

Asmussen and Lehtomaa [Distinguishing log-concavity from heavy tails. Risks 5(10), 2017] introduced an interesting function $g$ which is able to distinguish between log-convex and log-concave tail behaviour of distributions, and proposed a…

Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…

Let $(X_1,Y_1),\ldots,(X_n,Y_n)$ be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise…

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…

This paper investigates pooling strategies for tail index and extreme quantile estimation from heavy-tailed data. To fully exploit the information contained in several samples, we present general weighted pooled Hill estimators of the tail…

The aim of this paper is to establish the asymptotic behavior of the mutual influence of the Gini index and the poverty measures by using the Gaussian fields described in Mergane and Lo(2013). The results are given as representation…

We develop a new extreme value theory for repeated cross-sectional and panel data to construct asymptotically valid confidence intervals (CIs) for conditional extremal quantiles from a fixed number $k$ of nearest-neighbor tail observations.…

We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a…

We propose a transformation capable of altering the tail properties of a distribution, motivated by extreme value theory, which can be used as a layer in a normalizing flow to approximate multivariate heavy tailed distributions. We apply…

Asymptotic theory of tail index estimation has been studied extensively in the frequentist literature on extreme values, but rarely in the Bayesian context. We investigate whether popular Bayesian kernel mixture models are able to support…

In the "stochastic $\delta N$ formalism", the statistics of the inflationary density perturbation are obtained from the first passage distribution of a stochastic process. We develop a general framework in which to evaluate the rare tail of…

The properties of Maximum Likelihood estimator in mixed causal and noncausal models with a generalized Student's t error process are reviewed. Several known existing methods are typically not applicable in the heavy-tailed framework. To…

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…

It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…

We show, both analytically and numerically, that non-Gaussian tails in the probability density function of curvature perturbations arise in ultra-slow-roll inflation from the $\delta N$ formalism, without invoking stochastic inflation.…

Extreme U-statistics arise when the kernel of a U-statistic has a high degree but depends only on its arguments through a small number of top order statistics. As the kernel degree of the U-statistic grows to infinity with the sample size,…

Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modeling the power-law tails of the…

The Gini coefficient, a non-parametric measure of galaxy morphology, has recently taken up an important role in the automated identification of galaxy mergers. I present a critical assessment of its stability, based on a comparison of…

Growth mixture models (GMMs) incorporate both conventional random effects growth modeling and latent trajectory classes as in finite mixture modeling; therefore, they offer a way to handle the unobserved heterogeneity between subjects in…

We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…