Related papers: Maximum likelihood estimation for discrete exponen…
Bogdan et al. established a new criterion to determine the existence of a maximum likelihood estimator in discrete exponential families. It uses the notion of the set of uniqueness, which allows to apply the problem to the Ising model from…
The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric…
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…
We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…
We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the $\beta$-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based…
The {\lambda}-exponential family has recently been proposed to generalize the exponential family. While the exponential family is well-understood and widely used, this it not the case of the {\lambda}-exponential family. However, many…
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…
Providing theoretical guarantees for parameter estimation in exponential random graph models is a largely open problem. While maximum likelihood estimation has theoretical guarantees in principle, verifying the assumptions for these…
The use of continuous probability distributions has been widespread in problems with purely discrete nature. In general, such distributions are not appropriate in this scenario. In this paper, we introduce a class of discrete and asymmetric…
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…
We present a streamlined proof of the foundational result in the theory of exponential random graph models (ERGMs) that the maximum likelihood estimate exists if and only if the target statistic lies in the relative interior of the convex…
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…
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…
Inspired by applications to theories of coding and communication in networks of nervous tissue, we study maximum entropy distributions on weighted graphs with a given expected degree sequence. These distributions are characterized by…
Maximum likelihood estimation is effective for identifying dynamical systems, but applying it to large networks becomes computationally prohibitive. This paper introduces a maximum likelihood estimation method that enables identification of…
In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…
This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…
We consider discrete graphical models Markov with respect to a graph $G$ and propose two distributed marginal methods to estimate the maximum likelihood estimate of the canonical parameter of the model. Both methods are based on a…
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…
As is the case for many curved exponential families, the computation of maximum likelihood estimates in a multivariate normal model with a Kronecker covariance structure is typically carried out with an iterative algorithm, specifically, a…