Related papers: Global and Tail Dependence: A Differential Geometr…
Conditional Kendall's tau is a measure of dependence between two random variables, conditionally on some covariates. We assume a regression-type relationship between conditional Kendall's tau and some covariates, in a parametric setting…
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…
For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…
Accurately quantifying tail risks-rare but high-impact events such as financial crashes or extreme weather-is a central challenge in risk management, with serially dependent data. We develop a Bayesian framework based on the Generalized…
Regression analysis is one of the most popularly used statistical technique which only measures the direct effect of independent variables on dependent variable. Path analysis looks for both direct and indirect effects of independent…
Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…
The replacement of indicator functions by integrated beta kernels in the definition of the empirical stable tail dependence function is shown to produce a smoothed version of the latter estimator with the same asymptotic distribution but…
Measuring a strength of dependence of random variables is an important problem in statistical practice. In this paper, we propose a new function valued measure of dependence of two random variables. It allows one to study and visualize…
Following our previous work on copula-based nonsymmetric bivariate dependence measures, we propose a new set of conditions on nonsymmetric multivariate dependence measures which characterize both independence and complete dependence of one…
Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…
Real-world data are long-tailed, the lack of tail samples leads to a significant limitation in the generalization ability of the model. Although numerous approaches of class re-balancing perform well for moderate class imbalance problems,…
We consider the problem of supervised dimension reduction with a particular focus on extreme values of the target $Y\in\mathbb{R}$ to be explained by a covariate vector $X \in \mathbb{R}^p$. The general purpose is to define and estimate a…
Dependence modeling of multivariate count data has garnered significant attention in recent years. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of…
Classical information-theoretic generalization bounds typically control the generalization gap through KL-based mutual information and therefore rely on boundedness or sub-Gaussian tails via the moment generating function (MGF). In many…
Reinforcement learning is a framework for interactive decision-making with incentives sequentially revealed across time without a system dynamics model. Due to its scaling to continuous spaces, we focus on policy search where one…
This paper addresses the advancement of probability tail bound analysis, a crucial statistical tool for assessing the probability of large deviations of random variables from their expected values. Traditional tail bounds, such as Markov's,…
The normal distribution and its perturbation has left an immense mark on the statistical literature. Hence, several generalized forms were developed to model different skewness, kurtosis, and body shapes. However, it is not easy to…
Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to…
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
We propose a Gaussian-copula-based framework that learns deal-level dependence directly from observed joint success frequencies across founder, geography, and market attributes. Holding marginal deal success probabilities fixed, deal-level…