Related papers: Taming the Long Tail of Deep Probabilistic Forecas…
The increasing penetration of embedded renewables makes forecasting net-load, consumption less embedded generation, a significant and growing challenge. Here a framework for producing probabilistic forecasts of net-load is proposed with…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
The upper tail of a claim size distribution of a property line of business is frequently modelled by Pareto distribution. However, the upper tail does not need to be Pareto distributed, extraordinary shapes are possible. Here, the…
Kurtosis is seen as a measure of the discrepancy between the observed data and a Gaussian distribution and is defined when the 4th moment is finite. In this work an empirical study is conducted to investigate the behaviour of the sample…
Probabilistic forecasts are typically obtained using state-of-the-art statistical and machine learning models, with model parameters estimated by optimizing a proper scoring rule over a set of training data. If the model class is not…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
This paper compares the accuracy of tail risk forecasts with a focus on including realized skewness and kurtosis in "additive" and "multiplicative" models. Utilizing a panel of 960 US stocks, we conduct diagnostic tests, employ scoring…
Learning-based solutions for long-tailed recognition face difficulties in generalizing on balanced test datasets. Due to imbalanced data prior, the learned \textit{a posteriori} distribution is biased toward the most frequent (head)…
In this paper we develop a novel inferential approach based on geometric records for estimating the tail index of heavy-tailed distributions. We construct a maximum likelihood estimator for the Pareto model and establish its strong…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…
This work proposes a novel method to robustly and accurately model time series with heavy-tailed noise, in non-stationary scenarios. In many practical application time series have heavy-tailed noise that significantly impacts the…
A typical trajectory planner of autonomous driving commonly relies on predicting the future behavior of surrounding obstacles. Recently, deep learning technology has been widely adopted to design prediction models due to their impressive…
Forecast combination has been proven to be a very important technique to obtain accurate predictions. In many applications, forecast errors exhibit heavy tail behaviors for various reasons. Unfortunately, to our knowledge, little has been…
By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
Predicting the future trajectories of the traffic agents is a gordian technique in autonomous driving. However, trajectory prediction suffers from data imbalance in the prevalent datasets, and the tailed data is often more complicated and…
Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to MLE become…