Related papers: When does the mean excess plot look linear?

Cross-validation is a widely-used technique to estimate prediction error, but its behavior is complex and not fully understood. Ideally, one would like to think that cross-validation estimates the prediction error for the model at hand, fit…

We fit the exponent of the Pareto distribution, that is equivalent or can approximate the continuous power law distribution given a cutoff point, using linear regression (LR). We use LR on the logged variables of the empirical tail (one…

We derive a new class of statistical tests for generalized linear models based on thresholding point estimators. These tests can be employed whether the model includes more parameters than observations or not. For linear models, our tests…

In most risk assessment studies, it is important to accurately capture the entire distribution of the multivariate random vector of interest from low to high values. For example, in climate sciences, low precipitation events may lead to…

Overplotted line charts can obscure trends in temporal data and hinder prediction. We conduct a user study comparing three alternatives-aggregated, trellis, and spiral line charts against standard line charts on tasks involving trend…

Empirical Bayes estimators are based on minimizing the average risk with the hyper-parameters in the weighting function being estimated from observed data. The performance of an empirical Bayes estimator is typically evaluated by its mean…

In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a…

Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…

A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…

Colored graphical models provide a parsimonious approach to modeling high-dimensional data by exploiting symmetries in the model parameters. In this work, we introduce the notion of coloring for extremal graphical models on multivariate…

Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…

Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…

In this paper, we use the modern setting of functional empirical processes and recent techniques on uniform estimation for non parametric objects to derive consistency bands for the mean excess function in the i.i.d. case. We apply our…

Model analysis provides a mechanism for representing student learning as measured by standard multiple-choice surveys. The model plot contains information regarding both how likely students in a particular class are to choose the correct…

Pareto distributions are widely used models in economics, finance and actuarial sciences. As a result, a number of goodness-of-fit tests have been proposed for these distributions in the literature. We provide an overview of the existing…

Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows…

Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…

In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode…