Related papers: The multivariate tail-inflated normal distribution…
Generating synthetic financial time series that preserve the statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches struggle to simultaneously reproduce…
The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…
Tail risk protection is in the focus of the financial industry and requires solid mathematical and statistical tools, especially when a trading strategy is derived. Recent hype driven by machine learning (ML) mechanisms has raised the…
We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$…
Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…
Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…
This paper proposes methods for Bayesian inference in time-varying parameter (TVP) quantile regression (QR) models featuring conditional heteroskedasticity. I use data augmentation schemes to render the model conditionally Gaussian and…
Motivated by a bidimensional discrete-time risk model in insurance, we study the second-order asymptotics for two kinds of tail probabilities of the stochastic discounted value of aggregate net losses including two business lines. These are…
Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a…
In this paper we introduce a bivariate distribution on $\mathbb{R}_{+} \times \mathbb{N}$ arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively,…
In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale under norming sequence 1/n, as in the classical Law of Large Numbers (LLN), by means of martingale differences…
In this paper we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF)…
This paper contains sharp estimates about the distribution of multiple random integrals of functions of several variables with respect to a normalized empirical measure, about the distribution of U-statistics and multiple Wiener-Ito…
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
Economically responsible mitigation of multivariate extreme risks-such as extreme rainfall over large areas, large simultaneous variations in many stock prices, or widespread breakdowns in transportation systems-requires assessing the…
In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture…
This paper considers deep visual recognition on long-tailed data. To be general, we consider two applied scenarios, \ie, deep classification and deep metric learning. Under the long-tailed data distribution, the majority classes (\ie, tail…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
For stationary interface growth, governed by the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik-Rains distribution. Recently Chhita et al. [1]…