arXiv subjects

László Viharos

Publications and source records attributed to László Viharos.

4 recordsLinked to original sources

arXiv2025

Generalized Rényi statistics

In Rényi's representation for exponential order statistics, we replace the iid exponential sequence with any iid sequence, and call the resulting order statistic generalized Rényi statistic. We prove that by randomly reordering the variables in the generalized Rényi statistic, we obtain in the limit a sequence of iid exponentials. This result allows us to propose a new model for heavy-tailed data. Although the new model is very close to the classical iid framework, we establish that the Hill estimator is weakly consistent and asymptotically normal without any further assumptions on the underlying distribution or on the number of upper order statistics used in the estimator.

math.ST↗

arXiv2021

Asymptotic distributions for weighted power sums of extreme values

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 $γ$. Given known constants $d_{i,n}$, $1\le i\le n$, consider the weighted power sums $\sum^{k_n}_{i=1}d_{n+1-i,n}\log^pX_{n+1-i,n}$, where $p>0$ and the $k_n$ are positive integers such that $k_n\to\infty$ and $k_n/n\to0$ as $n\to\infty$. Under some constraints on the weights $d_{i,n}$, we prove asymptotic normality for the power sums over the whole heavy-tail model. We apply the obtained result to construct a new class of estimators for the parameter $γ$.

math.PR↗

arXiv2020

Weighted least squares estimators for the Parzen tail index

Estimation of the tail index of heavy-tailed distributions and its applications are essential in many research areas. We propose a class of weighted least squares (WLS) estimators for the Parzen tail index. Our approach is based on the method developed by \cite{Holan2010}. We investigate consistency and asymptotic normality of the WLS estimators. Through a simulation study, we make a comparison with the Hill, Pickands, DEdH (Dekkers, Einmahl and de Haan) and ordinary least squares (OLS) estimators using the mean square error as criterion. The results show that in a restricted model some members of the WLS estimators are competitive with the Pickands, DEdH and OLS estimators.

math.ST↗

arXiv2020

Regression estimators for the tail index

We propose a class of weighted least squares estimators for the tail index of a distribution function with a regularly varying upper tail. Our approach is based on the method developed by \cite{Holan2010} for the Parzen tail index. Asymptotic normality of the estimators is proved. Through a simulation study, these and earlier estimators are compared in the Pareto and Hall models using the mean squared error as criterion. The results show that the weighted least squares estimator is better than the other estimators investigated.

math.ST↗