Related papers: Multivariate saddlepoint approximations in tail pr…
We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…
The challenges posed by complex stochastic models used in computational ecology, biology and genetics have stimulated the development of approximate approaches to statistical inference. Here we focus on Synthetic Likelihood (SL), a…
Joint models are well suited to modelling linked data from laboratories and health registers. However, there are few examples of joint models that allow for (a) multiple markers, (b) multiple survival outcomes (including terminal events,…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
In this paper, we study estimates on tail probabilities $\mathbb{P}(S_r \ge t)$ of several classes of subordinators under mild assumptions on the tail of its L\'evy measure. As an application of that result, we obtain two-sided estimates…
In the world of multivariate extremes, estimation of the dependence structure still presents a challenge and an interesting problem. A procedure for the bivariate case is presented that opens the road to a similar way of handling the…
This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…
The estimation of conditional quantiles at extreme tails is of great interest in numerous applications. Various methods that integrate regression analysis with an extrapolation strategy derived from extreme value theory have been proposed…
We address the problem of causal effect estimation where hidden confounders are present, with a focus on two settings: instrumental variable regression with additional observed confounders, and proxy causal learning. Our approach uses a…
Motivated by the prominence of Conditional Value-at-Risk (CVaR) as a measure for tail risk in settings affected by uncertainty, we develop a new formula for approximating CVaR based optimization objectives and their gradients from limited…
The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…
We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We…
We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on certain sets of parameters. We consider some applications…
For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable.…
Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…
Models with a large number of latent variables are often used to fully utilize the information in big or complex data. However, they can be difficult to estimate using standard approaches, and variational inference methods are a popular…