Related papers: Fixed Point Iteration for Estimating The Parameter…
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…
This paper investigates a change-point estimation problem in the context of high-dimensional Markov Random Field models. Change-points represent a key feature in many dynamically evolving network structures. The change-point estimate is…
The maximum likelihood method offers a standard way to estimate the three parameters of a generalized extreme value (GEV) distribution. Combined with the block maxima method, it is often used in practice to assess the extreme value index…
Extreme value applications commonly employ regression techniques to capture cross-sectional heterogeneity or time-variation in the data. Estimation of the parameters of an extreme value regression model is notoriously challenging due to the…
For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach…
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…
This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stable (or max-infinitely divisible) process $\{\eta(t)\}_{t\in T}$ given…
Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…
We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various…
This paper proposes a novel method to estimate the rate parameter of the Poisson distribution. The proposed method employs the Cramer-von Mises type optimization which has been commonly used in estimating parameters of continuous…
Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for 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…
Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no…
Mixtures of $r$ independent distributions for two discrete random variables can be represented by matrices of nonnegative rank $r$. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry…
One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…
The problem of determining the (least) fixpoint of (higher-dimensional) functions over the non-negative reals frequently occurs when dealing with systems endowed with a quantitative semantics. We focus on the situation in which the…
We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…
A common approach for modeling extremes, such as peak flow or high temperatures, is the three-parameter Generalized Extreme-Value distribution. This is typically fit to extreme observations, here defined as maxima over disjoint blocks. This…