Related papers: Maximum likelihood estimation for the Fr\'echet di…
The block maxima (BM) approach in extreme value analysis fits a sample of block maxima to the Generalized Extreme Value (GEV) distribution. We consider all potential blocks from a sample, which leads to the All Block Maxima (ABM) estimator.…
We develop Stein's method for the Fr\'echet distribution and apply it to compute rates of convergence in distribution of renormalized sample maxima to the Fr\'echet distribution.
Parametric inference for spatial max-stable processes is difficult since the related likelihoods are unavailable. A composite likelihood approach based on the bivariate distribution of block maxima has been recently proposed in the…
In this paper we consider the estimation problem for high quantiles of a heavy-tailed distribution from block data when only a few largest values are observed within blocks. We propose estimators for high quantiles and prove that these…
One of the most common anticipated difficulties in applying mainstream maximum likelihood inference upon extreme values is articulated on the scarcity of extreme observations for bringing the extreme value theorem to hold across a series of…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…
This paper develops a rigorous asymptotic framework for likelihood-based inference in the Block Maxima (BM) method for stationary time series. While Bayesian inference under the BM approach has been widely studied in the independence…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
The H\"usler-Reiss distribution describes the limit of the pointwise maxima of a bivariate normal distribution. This distribution is defined by a single parameter, $\lambda$. We provide asymptotic theory for maximum likelihood estimation of…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…
In this article, we consider the problem of estimating the parameters of the Fr\'echet distribution from both frequentist and Bayesian points of view. First we briefly describe different frequentist approaches, namely, maximum likelihood,…
The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to…
The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…
The block maxima approach is an important method in univariate extreme value analysis. While assuming that block maxima are independent results in straightforward analysis, the resulting inferences maybe invalid when a series of block…
In this paper we show that the so-called array Fr\'echet problem in Probability/Statistics is (max, +)-linear. The upper bound of Fr\'echet is obtained using simple arguments from residuation theory and lattice distributivity. The lower…
Classical extreme value statistics consists of two fundamental approaches: the block maxima (BM) method and the peak-over-threshold (POT) approach. It seems to be general consensus among researchers in the field that the POT method makes…
We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…
Full likelihood-based inference for high-dimensional multivariate extreme value distributions, or max-stable processes, is feasible when incorporating occurrence times of the maxima; without this information, $d$-dimensional likelihood…
Software for computation of maximum likelihood estimates in linear structural equation models typically employs general techniques from non-linear optimization, such as quasi-Newton methods. In practice, careful tuning of initial values is…