Related papers: Efficient inference about the tail weight in multi…

We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…

We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…

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…

The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…

A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…

We show how to reduce the problem of computing VaR and CVaR with Student T return distributions to evaluation of analytical functions of the moments. This allows an analysis of the risk properties of systems to be carefully attributed…

We employ a general Monte Carlo method to test composite hypotheses of goodness-of-fit for several popular multivariate models that can accommodate both asymmetry and heavy tails. Specifically, we consider weighted L2-type tests based on a…

Student's $t$ statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, for example robustness against heavy tailed sampling…

Heavy tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with Internet transaction datasets, and machine learners often analyze such data without considering the biases…

We present a new Monte Carlo methodology for the accurate estimation of the distribution of the sum of dependent log-normal random variables. The methodology delivers statistically unbiased estimators for three distributional quantities of…

This paper develops an efficient Monte Carlo method to estimate the tail probabilities of the ratio of the largest eigenvalue to the trace of the Wishart matrix, which plays an important role in multivariate data analysis. The estimator is…

We propose estimating the scale parameter (mean of the eigenvalues) of the scatter matrix of an unspecified elliptically symmetric distribution using weights obtained by solving Tyler's M-estimator of the scatter matrix. The proposed…

We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we…

We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail…

Markov switching models are often used to analyze financial returns because of their ability to capture frequently observed stylized facts. In this paper we consider a multivariate Student-t version of the model as a viable alternative to…

We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…

We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well as incorrect…

How to estimate the uncertainty of a given model is a crucial problem. Current calibration techniques treat different classes equally and thus implicitly assume that the distribution of training data is balanced, but ignore the fact that…

The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are as follows: (1) the study is nonasymptotic, that is, the sample size is fixed and does not…

Adaptive importance sampling (AIS) algorithms are widely used to approximate expectations with respect to complicated target probability distributions. When the target has heavy tails, existing AIS algorithms can provide inconsistent…