Related papers: Efficient simulation for dependent rare events wit…
A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…
In this paper, we consider a classic problem concerning the high excursion probabilities of a Gaussian random field $f$ living on a compact set $T$. We develop efficient computational methods for the tail probabilities $P(\sup_T f(t) > b)$…
We develop importance sampling based efficient simulation techniques for three commonly encountered rare event probabilities associated with random walks having i.i.d. regularly varying increments; namely, 1) the large deviation…
Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…
Solving decision problems in complex, stochastic environments is often achieved by estimating the expected outcome of decisions via Monte Carlo sampling. However, sampling may overlook rare, but important events, which can severely impact…
We study robust estimators of the mean of a probability measure $P$, called robust empirical mean estimators. This elementary construction is then used to revisit a problem of aggregation and a problem of estimator selection, extending…
This study provides a summary of the theory which enables the analysis of extreme values, i.e., of measurements acquired from the observation of extraordinary/rare physical phenomena. The formalism is developed in a transparent way,…
This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions…
In this manuscript, we investigate importance sampling methods for rare-event simulation in diffusion processes. We show, from a large-deviation perspective, that the resulting importance sampling estimator is log-efficient. This connection…
We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian,…
This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…
We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…
One of the goals of climate science is to characterize the statistics of extreme and potentially dangerous events in the present and future climate. Extreme events like heat waves, droughts, or floods due to persisting rains are…
This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
Large language model-powered multi-agent systems have emerged as powerful tools for simulating complex human-like systems. The interactions within these systems often lead to extreme events whose origins remain obscured by the black box of…
In this paper, we propose an efficient importance sampling algorithm for rare event simulation under copula models. In the algorithm, the derived optimal probability measure is based on the criterion of minimizing the variance of the…
Importance sampling (IS) is a widely used simulation method for estimating rare event probabilities. In IS, the relative variance of an estimator is the most common measure of estimator accuracy, and the focus of existing literature is on…
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…
We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…
We obtain error terms on the rate of convergence to Extreme Value Laws for a general class of weakly dependent stochastic processes. The dependence of the error terms on the `time' and `length' scales is very explicit. Specialising to data…