Related papers: Maximum likelihood estimation for matrix normal mo…
Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…
We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently…
Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…
The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a cornerstone of statistical theory. In the present paper, we provide sharp explicit upper bounds on Zolotarev-type distances between the exact, unknown distribution of…
The maximum likelihood degree (ML degree) measures the algebraic complexity of a fundamental optimization problem in statistics: maximum likelihood estimation. In this problem, one maximizes the likelihood function over a statistical model.…
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase transition'. We introduce an explicit boundary…
Maximum likelihood estimators (MLE) and control variate estimators (CVE) have been used in conjunction with known information across sketching algorithms and applications in machine learning. We prove that under certain conditions in an…
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to…
For the univariate current status and, more generally, the interval censoring model, distribution theory has been developed for the maximum likelihood estimator (MLE) and smoothed maximum likelihood estimator (SMLE) of the unknown…
It is well known that under general regularity conditions the distribution of the maximum likelihood estimator (MLE) is asymptotically normal. Very recently, bounds of the optimal order $O(1/\sqrt n)$ on the closeness of the distribution of…
Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we…
We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in $\mathbb{R}^d$. Our study covers both the case where the true underlying density is…
In this paper a useful subfamily of the exponential family has been considered. The ML estimation based on upper record values has been calculated for the parameter, Cumulative Density Function, and Probability Density Function of the…
Modern machine learning embeddings provide powerful compression of high-dimensional data, yet they typically destroy the geometric structure required for classical likelihood-based statistical inference. This paper develops a rigorous…
This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…
Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general. It includes pairwise pair potentials, finite and infinite multibody interactions and…
We show that the method of maximum-likelihood estimation, recently introduced in the context of quantum process tomography, can be applied to the determination of Mueller matrices characterizing the polarization properties of classical…
We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over…
Maximum likelihood estimation (MLE) is the most common approach to quantum state tomography. In this letter, we investigate whether it is also optimal in any sense. We show that MLE is an inadmissible estimator for most of the commonly used…
Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…