Related papers: How to (Not) Estimate Gini Coefficients for Fat Ta…

The Gini score is a popular tool in statistical modeling and machine learning for model validation and model selection. It is a purely rank based score that allows one to assess risk rankings. The Gini score for statistical modeling has…

In this paper, we consider the problem of the estimation of a Weibull tail-coefficient. In particular, we propose a regression model, from which we derive a bias-reduced estimator. This estimator is based on a least-squares approach. The…

In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal…

The Weibull tail-coefficient (WTC) plays a crucial role in extreme value statistics when dealing with Weibull-type tails. Several distributions, such as normal, Gamma, Weibull, and Logistic distributions, exhibit this type of tail…

In this paper a result of Latala about the tail behavior of Gaussian polynomials will be discussed. Latala proved an interesting result about this problem in paper [2]. But his proof applied an incorrect statement at a crucial point. Hence…

What do binary (or probabilistic) forecasting abilities have to do with overall performance? We map the difference between (univariate) binary predictions, bets and "beliefs" (expressed as a specific "event" will happen/will not happen) and…

Standard inference about a scalar parameter estimated via GMM amounts to applying a t-test to a particular set of observations. If the number of observations is not very large, then moderately heavy tails can lead to poor behavior of the…

Alpha-based performance evaluation may fail to capture correlated residuals due to model errors. This paper proposes using the Generalized Information Ratio (GIR) to measure performance under misspecified benchmarks. Motivated by the…

This paper introduces a flexible framework for the estimation of the conditional tail index of heavy tailed distributions. In this framework, the tail index is computed from an auxiliary linear regression model that facilitates estimation…

Heavy tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with Internet transaction datasets, and machine learners often analyze such data without considering the biases…

Risk measures, which typically evaluate the impact of extreme losses, are highly sensitive to misspecification in the tails. This paper studies a robust optimization approach to combat tail uncertainty by proposing a unifying framework to…

Count regression models are necessary for examining discrete dependent variables alongside covariates. Nonetheless, when data display outliers, overdispersion, and an abundance of zeros, traditional methods like the zero-inflated negative…

The inequality is computed through the so-called Gini index. The population is assumed to have the variable of interest distributed according to the Gamma probability distribution. The results show that the Gini index is reduced when the…

We propose a new measure related with tail dependence in terms of correlation: quantile correlation coefficient of random variables X, Y. The quantile correlation is defined by the geometric mean of two quantile regression slopes of X on Y…

We study the probability tail properties of Inverse Probability Weighting (IPW) estimators of the Average Treatment Effect (ATE) when there is limited overlap between the covariate distributions of the treatment and control groups. Under…

Many random phenomena, including life-testing and environmental data, show positive values and excess zeros, which pose modeling challenges. In life testing, immediate failures result in zero lifetimes, often due to defects or poor quality,…

We re-visit tail the index regressions framework. For linear specifications, we find that the usual full rank condition can fail because conditioning on extreme outcomes causes regressors to degenerate to constants. Taking this into…

Kink model is developed to analyze the data where the regression function is twostage linear but intersects at an unknown threshold. In quantile regression with longitudinal data, previous work assumed that the unknown threshold parameters…

In the presence of a layer of metaprobabilities (from uncertainty concerning the parameters), the asymptotic tail exponent corresponds to the lowest possible tail exponent regardless of its probability. The problem explains "Black Swan"…

Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…