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Modeling and understanding multivariate extreme events is challenging, but of great importance in various applications - e.g. in biostatistics, climatology, and finance. The separating Hill estimator can be used in estimating the extreme…
We study the connection between the appearance of a `metastable' behavior of weakly chaotic orbits, characterized by a constant rate of increase of the Tsallis q-entropy (Tsallis 1988), and the solutions of the variational equations of…
We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…
In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…
Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…
In 2017-2020 Jordanova and co-authors investigate probabilities for p-outside values and determine them in many particular cases. They show that these probabilities are closely related to the concept for heavy tails. Tukey's boxplots are…
In this paper, the local asymptotic estimation for the supremum of a random walk and its applications are presented. The summands of the random walk have common long-tailed and generalized strong subexponential distribution. This…
Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable…
A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…
The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail…
This article studies tail behavior for the error components in the stochastic frontier model, where one component has bounded support on one side, and the other has unbounded support on both sides. Under weak assumptions on the error…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…
Using a renormalization approach, we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power q(n) that varies monotonically with the sample size n.…
Many random phenomena, including life-testing and environmental data, show positive values and excess zeros, which pose modeling challenges. In life testing, immediate failures result in zero lifetimes, often due to defects or poor quality,…
Conditionally specified models are often used to describe complex multivariate data. Such models assume implicit structures on the extremes. So far, no methodology exists for calculating extremal characteristics of conditional models since…
Understanding random open quantum systems is critical for characterizing the performance of large-scale quantum devices and exploring macroscopic quantum phenomena. Various features in these systems, including spectral distributions, gap…
In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Here, we study the limiting behaviour of the mean residual life, and derive an asymptotic expansion which can be used…
Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities…
We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limiting process observed at the same time point. To keep track…
We consider the moderate deviations behaviors for two (co-) volatility estima-tors: generalised bipower variation, Hayashi-Yoshida estimator. The results are obtained by using a new result about the moderate deviations principle for…