相关论文: When does the mean excess plot look linear?

The downside risk of a portfolio of (equity)assets is generally substantially higher than the downside risk of its components. In particular in times of crises when assets tend to have high correlation, the understanding of this difference…

Scatterplots can encode a third dimension by using additional channels like size or color (e.g. bubble charts). We explore a potential misinterpretation of trivariate scatterplots, which we call the weighted average illusion, where…

Machine learning applications frequently come with multiple diverse objectives and constraints that can change over time. Accordingly, trained models can be tuned with sets of hyper-parameters that affect their predictive behavior (e.g.,…

The processes of the averaged regression quantiles and of their modifications provide useful tools in the regression models when the covariates are not fully under our control. As an application we mention the probabilistic risk assessment…

We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…

Properties of weighted averages are studied for the general case that the individual measurements are subject to hidden correlations and have asymmetric statistical as well as systematic errors. Explicit expressions are derived for an…

The Extended Generalized Pareto Distribution (EGPD) (Naveau et al. 2016) is a family of distribution that has been introduced to model the full range of a positive random variable but with the lower and the upper tails distributed according…

Consider a linear regression model with independent and identically normally distributed random errors. Suppose that the parameter of interest is a specified linear combination of the regression parameters. We prove that the usual…

We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and…

The popular generalized additive model framework is extended to allow both the mean curves and the response distribution to be nonparametric. The approach is demonstrated to be a flexible yet parsimonious tool for data analysis in its own…

This paper introduces two families of probability distributions for Bayesian analysis of hypertoroidal data. The first family consists of symmetric distributions derived from the projection of multivariate normal distributions under…

In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using…

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…

We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard…

A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…

We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or…

We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The…

Neural networks are able to approximate any continuous function on a compact set. However, it is not obvious how to quantify the error of the neural network, i.e., the remaining bias between the function and the neural network. Here, we…

The Bayes linear estimator is derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as ordinary ridge, typical shrinkage, fractional rank, and restricted least squares estimators, as…

In samples from a heavy-tailed distribution a second-order approximation is often use to approximate the tail function. Based on the parameters of the approximation, an optimal sample fraction can be estimated which is then used to estimate…