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Asmussen and Lehtomaa [Distinguishing log-concavity from heavy tails. Risks 5(10), 2017] introduced an interesting function $g$ which is able to distinguish between log-convex and log-concave tail behaviour of distributions, and proposed a…

Methodology · Statistics 2023-07-25 Toshiya Iwashita , Bernhard Klar

Expectiles define the only law-invariant, coherent and elicitable risk measure apart from the expectation. The popularity of expectile-based risk measures is steadily growing and their properties have been studied for independent data, but…

Methodology · Statistics 2021-10-13 Anthony C. Davison , Simone A. Padoan , Gilles Stupfler

We consider the problem of efficient simulation estimation of the density function at the tails, and the probability of large deviations for a sum of independent, identically distributed, light-tailed and non-lattice random vectors. The…

Probability · Mathematics 2017-04-26 Santanu Dey , Sandeep Juneja , Ankush Agarwal

We use the so-called t-Hill tail index estimator proposed by Fabi\'an(2001), rather than Hill's one, to derive a robust estimator for the distortion risk premium of loss. Under the second-order condition of regular variation, we establish…

Statistics Theory · Mathematics 2016-02-16 Brahim Brahimi , Zoubir Kenioua

We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of…

Probability · Mathematics 2009-06-29 Abhimanyu Mitra , Sidney I. Resnick

In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a…

Risk Management · Quantitative Finance 2023-04-12 Bikramjit Das , Vicky Fasen-Hartmann

Uncertainty requires suitable techniques for risk assessment. Combining stochastic approximation and stochastic average approximation, we propose an efficient algorithm to compute the worst case average value at risk in the face of tail…

Risk Management · Quantitative Finance 2022-01-19 Sojung Kim , Stefan Weber

Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models.…

Methodology · Statistics 2024-09-05 Wentao Li , Rosabeth White , Dennis Prangle

Consider a random walk whose (light-tailed) increments have positive mean. Lower and upper bounds are provided for the expected maximal value of the random walk until it experiences a given drawdown d. These bounds, related to the Calmar…

Probability · Mathematics 2008-07-23 Isaac Meilijson

The entropic risk measure is widely used in high-stakes decision-making across economics, management science, finance, and safety-critical control systems because it captures tail risks associated with uncertain losses. However, when data…

Optimization and Control · Mathematics 2026-01-05 Utsav Sadana , Erick Delage , Angelos Georghiou

We propose a restricted win probability estimand for comparing treatments in a randomized trial with a time-to-event outcome. We also propose Bayesian estimators for this summary measure as well as the unrestricted win probability. Bayesian…

Methodology · Statistics 2024-11-06 Michelle Leeberg , Xianghua Luo , Thomas A. Murray

We consider importance sampling for estimating the probability that a light-tailed $d$-dimensional random walk exits through one of many disjoint rare-event regions before reaching an anticipated target. This problem arises in sequential…

Probability · Mathematics 2025-09-19 Yanglei Song , Georgios Fellouris

Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of…

Probability · Mathematics 2012-10-09 Robert J. Adler , Jose H. Blanchet , Jingchen Liu

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…

Statistics Theory · Mathematics 2026-02-10 Jiming Jiang , Matt P. Wand , Swarnadip Ghosh

Intelligent systems are increasingly integral to our daily lives, yet rare safety-critical events present significant latent threats to their practical deployment. Addressing this challenge hinges on accurately predicting the probability of…

Machine Learning · Computer Science 2024-04-08 Ruoxuan Bai , Jingxuan Yang , Weiduo Gong , Yi Zhang , Qiujing Lu , Shuo Feng

Let $X$ be the number of $k$-term arithmetic progressions contained in the $p$-biased random subset of the first $N$ positive integers. We give asymptotically sharp estimates on the logarithmic upper-tail probability $\log \Pr(X \ge E[X] +…

Probability · Mathematics 2024-09-16 Matan Harel , Frank Mousset , Wojciech Samotij

The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an…

Computation · Statistics 2013-10-15 Z. I. Botev , A. Ridder , L. Rojas-Nandayapa

In this paper, we compare two numerical methods for approximating the probability that the sum of dependent regularly varying random variables exceeds a high threshold under Archimedean copula models. The first method is based on…

Computation · Statistics 2017-08-31 Hélène Cossette , Etienne Marceau , Quang Huy Nguyen , Christian Robert

Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are…

Robotics · Computer Science 2023-02-22 Khaled A. Mustafa , Oscar de Groot , Xinwei Wang , Jens Kober , Javier Alonso-Mora

On the basis of Nelson-Aalen nonparametric estimator of the cumulative distribution function, we provide a weak approximation to tail product-limit process for randomly right-censored heavy-tailed data. In this context, a new consistent…

Statistics Theory · Mathematics 2016-07-25 Brahim Brahimi , Djamel Meraghni , Abdelhakim Necir