Related papers: Estimation of Expected Shortfall under Various Exp…
Expected shortfall (ES), also known as conditional value-at-risk, is a widely recognized risk measure that complements value-at-risk by capturing tail-related risks more effectively. Compared with quantile regression, which has been…
Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected…
Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used…
To answer questions of "causes of effects", the probability of necessity is introduced for assessing whether or not an observed outcome was caused by an earlier treatment. However, the statistical inference for probability of necessity is…
The Expected Shortfall (ES) is one of the most important regulatory risk measures in finance, insurance, and statistics, which has recently been characterized via sets of axioms from perspectives of portfolio risk management and statistics.…
Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the…
Payments in parametric insurance solutions are linked to an index and thus decoupled from policyholders' true losses. While this principle has appealing operational benefits compared to traditional indemnity coverage, i.e. is very efficient…
Forecast evaluations aim to choose an accurate forecast for making decisions by using loss functions. However, different loss functions often generate different ranking results for forecasts, which complicates the task of comparisons. In…
The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures…
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…
To compare different forecasting methods on demand series we require an error measure. Many error measures have been proposed, but when demand is intermittent some become inapplicable, some give counter-intuitive results, and there is no…
This paper introduces novel backtests for the risk measure Expected Shortfall (ES) following the testing idea of Mincer and Zarnowitz (1969). Estimating a regression framework for the ES stand-alone is infeasible, and thus, our tests are…
The common practice for displaying error bars on distributions of numbers of events is confusing and can lead to incorrect conclusions. A proposal is made for a different style of presentation that more directly indicates the level of…
This paper assumes each individual in society has a random discount factor and assesses an intertemporal project using rank-dependent expected utility theory. We consider both the ex ante and the ex post approaches. For the former, we show…
How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…
Systemic risk measures have been shown to be predictive of financial crises and declines in real activity. Thus, forecasting them is of major importance in finance and economics. In this paper, we propose a new forecasting method for…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Measuring the contribution of a bank or an insurance company to overall systemic risk is a key concern, particularly in the aftermath of the 2007--2009 financial crisis and the 2020 downturn. In this paper, we derive worst-case and…
Recently attention has been drawn to practical problems with the use of unbounded Pareto distributions, for instance when there are natural upper bounds that truncate the probability tail. Aban, Meerschaert and Panorska (2006) derived the…
The statistical tests that are commonly used for detecting mean or median treatment effects suffer from low power when the two distribution functions differ only in the upper (or lower) tail, as in the assessment of the Total Sharp Score…