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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,…

In this work, we study the problem of distributed mean estimation with $1$-bit communication constraints when the variance is unknown. We focus on the specific case where each user has access to one i.i.d. sample drawn from a distribution…

The problem of accurate nonparametric estimation of distributional functionals (integral functionals of one or more probability distributions) has received recent interest due to their wide applicability in signal processing, information…

Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. In this paper, MLE for statistical models with discrete data is studied from an algebraic statistics viewpoint. A reformulation of the MLE problem in…

Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…

We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses models that accommodate, for example, transitivity, degree heterogenenity, and other stylized features often observed in real network…

We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the alphabet size $S$ is…

Estimating the size of hidden populations using Multiple Systems Estimation (MSE) is a critical task in quantitative sociology; however, practical application is often hindered by imperfect administrative data and computational constraints.…

In this paper the Gaussian quasi maximum likelihood estimator (GQMLE) is generalized by applying a transform to the probability distribution of the data. The proposed estimator, called measure-transformed GQMLE (MT-GQMLE), minimizes 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 estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…

The inherent bias pathology of the maximum likelihood (ML) estimation method is confirmed for models with unknown parameters $\theta$ and $\psi$ when MLE $\hat \psi$ is function of MLE $\hat \theta.$ To reduce $\hat \psi$'s bias the…

For the tree topology, previous studies show the maximum likelihood estimate (MLE) of a link/path takes a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since then, the main concern…

Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…

We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with…

In a regular full exponential family, the maximum likelihood estimator (MLE) need not exist in the traditional sense. However, the MLE may exist in the completion of the exponential family. Existing algorithms for finding the MLE in the…

The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…

We consider smooth nonparametric estimation of the incubation time distribution of COVID-19, in connection with the investigation of researchers from the National Institute for Public Health and the Environment (Dutch: RIVM) of 88 travelers…

Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate…

This study uses controlled simulations with known ground-truth parameters to evaluate how Distributional Latent Variable Models (DLVM) and Bayesian Distributional Active LEarning (DALE) perform in comparison to conventional Independent…