Related papers: Weighted approximations of tail copula processes w…
This paper introduces a copula-based model for independent but non-identically distributed data with heteroscedastic extremes marginal and changing tail dependence structures. We establish a unified framework for inference by proving the…
When modeling the distribution of a multivariate continuous random vector using the so-called \emph{copula approach}, it is not uncommon to have ties in the coordinate samples of the available data because of rounding or lack of measurement…
Extreme value theory has constructed asymptotic properties of the sample maximum. This study concerns probability distribution estimation of the sample maximum. The traditional approach is parametric fitting to the limiting distribution --…
Let $X_{1,n}\le\cdots\le X_{n,n}$ be the order statistics of $n$ independent random variables with a common distribution function $F$ having right heavy tail with tail index $\gamma$. Given known constants $d_{i,n}$, $1\le i\le n$, consider…
We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…
The Weibull tail-coefficient (WTC) plays a crucial role in extreme value statistics when dealing with Weibull-type tails. Several distributions, such as normal, Gamma, Weibull, and Logistic distributions, exhibit this type of tail…
We propose an extension of the regular Cox's proportional hazards model which allows the estimation of the probabilities of rare events. It is known that when the data are heavily censored at the upper end of the survival distribution, the…
We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root…
Our goal in this paper is to propose an alternative risk measure which takes into account the fluctuations of losses and possible correlations between random variables. This new notion of risk measures, that we call Copula Conditional Tail…
The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…
We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the…
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…
Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal…
Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenarios, models exhibiting heavy tails in the margins and…
We study the effect of approximation errors in assessing the extreme behavior of heavy-tailed random objects. We give conditions for the approximation error such that the standard asymptotic results hold for the classical Hill estimator and…
Regular vine sequences permit the organisation of variables in a random vector along a sequence of trees. Regular vine models have become greatly popular in dependence modelling as a way to combine arbitrary bivariate copulas into…
A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…
We evaluate the dependence among the margins of a random vector with Multivariate Extreme Value distribution throughout the expected value of a range and relate this coefficient of dependence with the multivariate tail dependence. Its…
Motivated by the growing interest in sound forecast evaluation techniques with an emphasis on distribution tails rather than average behaviour, we investigate a fundamental question arising in this context: Can statistical features of…
We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…