Related papers: Maximum likelihood estimators based on the block m…
The distribution of block maxima of sequences of independent and identically-distributed random variables is used to model extreme values in many disciplines. The traditional extreme value (EV) theory derives a closed-form expression for…
We consider a one dimensional sub-ballistic random walk evolving in a parametric i.i.d. random environment. We study the asymptotic properties of the maximum likelihood estimator (MLE) of the parameter based on a single observation of the…
Extreme value theory (EVT) is a statistical tool for analysis of extreme events. It has a strong theoretical background, however, we need to choose hyper-parameters to apply EVT. In recent studies of machine learning, techniques of choosing…
We give an asymptotic development of the maximum likelihood estimator (MLE), or any other estimator defined implicitly, in a way which involves the limiting behavior of the score and its higher-order derivatives. This development, which is…
We aim to analyze the behaviour of a finite-time stochastic system, whose model is not available, in the context of more rare and harmful outcomes. Standard estimators are not effective in making predictions about such outcomes due to their…
Machine learning is vital in high-stakes domains, yet conventional validation methods rely on averaging metrics like mean squared error (MSE) or mean absolute error (MAE), which fail to quantify extreme errors. Worst-case prediction…
Boltzmann machines (BMs) are a class of binary neural networks for which there have been numerous proposed methods of estimation. Recently, it has been shown that in the fully visible case of the BM, the method of maximum pseudolikelihood…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements…
The normality assumption on data set is very restrictive approach for modelling. The generalized form of normal distribution, named as an exponential power (EP) distribution, and its scale mixture form have been considered extensively to…
This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…
The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of…
A critical problem in extreme value theory (EVT) is the estimation of parameters for the limit probability distributions. Block maxima (BM), an approach in EVT that seeks estimates of parameters of the generalized extreme value distribution…
Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…
The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory and is in common use for analyzing the far tail of observed phenomena. Curiously, important asymptotic properties of…
The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
Missing data occur in a variety of applications of extreme value analysis. In the block maxima approach to an extreme value analysis, missingness is often handled by either ignoring missing observations or dropping a block of observations…
Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations…
This paper introduces a novel sub-sampling block maxima technique to model and characterize environmental extreme risks. We examine the relationships between block size and block maxima statistics derived from the Gaussian and generalized…