Related papers: Several new tail index estimators
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
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…
This study examines the varying coefficient model in tail index regression. The varying coefficient model is an efficient semiparametric model that avoids the curse of dimensionality when including large covariates in the model. In fact,…
This paper investigates pooling strategies for tail index and extreme quantile estimation from heavy-tailed data. To fully exploit the information contained in several samples, we present general weighted pooled Hill estimators of the tail…
We consider a two dimensional skip-free reflecting random walk on a nonnegative integer quadrant. We are interested in the tail asymptotics of its stationary distribution, provided its existence is assumed. We derive exact tail asymptotics…
To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed nonparametric estimators of the spectral tail process. The methodology can be extended…
Let $X_{1,n} \leq .... \leq X_{n,n}$ be the order statistics associated with a sample $X_{1}, ...., X_{n}$ whose pertaining distribution function (% \textit{df}) is $F$. We are concerned with the functional asymptotic behaviour of the…
When studying treatment effects in multilevel studies, investigators commonly use (semi-)parametric estimators, which make strong parametric assumptions about the outcome, the treatment, and/or the correlation structure between study units…
In a recent article the authors obtained a formula which relates explicitly the tail of risk neutral returns with the wing behavior of the Black Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but…
Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as…
For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the…
Extremes occur in stationary regularly varying time series as short periods with several large observations, known as extremal blocks. We study cluster statistics summarizing the behavior of functions acting on these extremal blocks.…
A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized…
We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positive associated, which is modeled by the so-called tail dependent coefficient. We construct an estimator of…
By means of a Lynden-Bell integral with deterministic threshold, Worms and Worms [A Lynden-Bell integral estimator for extremes of randomly truncated data. Statist. Probab. Lett. 2016; 109: 106-117] recently introduced an asymptotically…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently…
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…
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…
In extreme value inference it is a fundamental problem how the target value is required to be extreme by the extreme value theory. In iid settings this study both theoretically and numerically compares tail estimators, which are based on…