Related papers: Maximum likelihood degree of variance component mo…

We consider constructing model selection criteria for evaluating nonlinear mixed effects models via basis expansions. Mean functions and random functions in the mixed effects model are expressed by basis expansions, then they are estimated…

We consider a finite mixture of regressions (FMR) model for high-dimensional inhomogeneous data where the number of covariates may be much larger than sample size. We propose an l1-penalized maximum likelihood estimator in an appropriate…

Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…

Latent variable models have been widely applied in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In…

Clustered data is ubiquitous in a variety of scientific fields. In this paper, we propose a flexible and interpretable modeling approach, called grouped heterogenous mixture modeling, for clustered data, which models cluster-wise…

Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model…

Real-data networks often appear to have strong modularity, or network-of-networks structure, in which subgraphs of various size and consistency occur. Finding the respective subgraph structure is of great importance, in particular for…

Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…

We settle a conjecture by Bik and Marigliano stating that the degree of a one-dimensional discrete model with rational maximum likelihood estimator is bounded above by a linear function in the size of its support, therefore showing that…

In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…

Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer models of the likelihood-to-evidence…

The design of optimal test statistics is a key task in frequentist statistics and for a number of scenarios optimal test statistics such as the profile-likelihood ratio are known. By turning this argument around we can find the profile…

Empirical economic research frequently applies maximum likelihood estimation in cases where the likelihood function is analytically intractable. Most of the theoretical literature focuses on maximum simulated likelihood (MSL) estimators,…

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…

The minimum number of observations such that the maximum likelihood estimator in a Gaussian graphical model exists with probability one is called the maximum likelihood threshold of the underlying graph G. The natural algebraic relaxation…

Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models.…

Multiple root estimation problems in statistical inference arise in many contexts in the literature. In the context of maximum likelihood estimation, the existence of multiple roots causes uncertainty in the computation of maximum…