Related papers: Toward a Hazard Rate Framework for Regular and Rap…
Hidden regular variation is a sub-model of multivariate regular variation and facilitates accurate estimation of joint tail probabilities. We generalize the model of hidden regular variation to what we call hidden domain of attraction. We…
In this paper, we consider finite mixture models with modified proportional hazard rates. Sufficient conditions for the usual stochastic order and the hazard order are established under chain majorization. We study stochastic comparisons…
We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic…
We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed…
Classical worst-case optimization theory neither explains the success of optimization in machine learning, nor does it help with step size selection. In this paper we demonstrate the viability and advantages of replacing the classical…
We introduce a class of short-rate models that exhibit a ``higher for longer'' phenomenon. Specifically, the short-rate is modeled as a general time-homogeneous one-factor Markov diffusion on a finite interval. The lower endpoint is assumed…
The objective is to model longitudinal and survival data jointly taking into account the dependence between the two responses in a real HIV/AIDS dataset using a shared parameter approach inside a Bayesian framework. We propose a linear…
Machine learning systems deployed in the real world must operate under dynamic and often unpredictable distribution shifts. This challenges the validity of statistical safety assurances on the system's risk established beforehand. Common…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
Survival analysis appears in various fields such as medicine, economics, engineering, and business. Recent studies showed that the Ordinary Differential Equation (ODE) modeling framework unifies many existing survival models while the…
We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic,…
Climate extremes such as floods, storms, and heatwaves have caused severe economic and human losses across Europe in recent decades. To support the European Union's climate resilience efforts, we propose a statistical framework for…
In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common…
Three statistical studies, all published between 2004 and 2008 but without referring to one another, assert a useful equivalence involving the hazard ratio, a parameter estimated for time to event data by the frequently used proportional…
We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…
Conditional extreme value models have been introduced by Heffernan and Resnick (2007) to describe the asymptotic behavior of a random vector as one specific component becomes extreme. Obviously, this class of models is related to classical…
Observed accidents have been the main resource for road safety analysis over the past decades. Although such reliance seems quite straightforward, the rare nature of these events has made safety difficult to assess, especially for new and…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…