English
Related papers

Related papers: Verifying the existence of maximum likelihood esti…

200 papers

Generalized linear models (GLMs) are popular for data-analysis in almost all quantitative sciences, but the choice of likelihood family and link function is often difficult. This motivates the search for likelihoods and links that minimize…

Methodology · Statistics 2024-03-19 Maximilian Scholz , Paul-Christian Bürkner

This paper introduces a high-dimensional binary variate model that accommodates nonstationary covariates and factors, and studies their asymptotic theory. This framework encompasses scenarios where single indices are nonstationary or…

Statistics Theory · Mathematics 2025-05-29 Xinbing Kong , Bin Wu , Wuyi Ye

Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…

Machine Learning · Statistics 2018-10-18 Rui Zhuang , Johannes Lederer

Suppose data are fitted to some parametric model but that the true model happens to be one with an additional parameter. When a parameter is to be estimated one can use likelihood estimation in the wider model or in the narrow model.…

Methodology · Statistics 2026-03-27 Nils Lid Hjort

Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…

Methodology · Statistics 2014-04-03 Adel Javanmard , Andrea Montanari

The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior…

Analysis of PDEs · Mathematics 2026-03-16 Chiun-Chang Lee

This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…

Statistics Theory · Mathematics 2016-06-06 W. T. M. Dunsmuir , J. Y. He

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…

Statistics Theory · Mathematics 2012-05-31 Jushan Bai , Kunpeng Li

We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study…

Statistics Theory · Mathematics 2019-09-04 Haolei Weng , Yang Feng

Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. In this paper, we study the asymptotic properties of maximum likelihood…

Statistics Theory · Mathematics 2012-07-27 Xiang Zhang , Yanbing Zheng

We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…

Statistics Theory · Mathematics 2008-11-24 Michel Broniatowski , Amor Keziou

Graphical and sparse (inverse) covariance models have found widespread use in modern sample-starved high dimensional applications. A part of their wide appeal stems from the significantly low sample sizes required for the existence of…

Statistics Theory · Mathematics 2023-11-28 Benjamin Roycraft , Bala Rajaratnam

We review Quasi Maximum Likelihood estimation of factor models for high-dimensional panels of time series. We consider two cases: (1) estimation when no dynamic model for the factors is specified (Bai and Li, 2012, 2016); (2) estimation…

Econometrics · Economics 2024-10-08 Matteo Barigozzi

Protesting mildly against the notion of an exactly correct parametric model the view is adopted that the logistic regression equation is merely an approximation to the underlying, true function. The behaviour of likelihood based estimators…

Statistics Theory · Mathematics 2026-05-27 Nils Lid Hjort

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…

Statistics Theory · Mathematics 2023-04-07 Henry Bayly , Aditya Khanna , Kathryn Lindsey

Nearly all statistical inference methods were developed for the regime where the number $N$ of data samples is much larger than the data dimension $p$. Inference protocols such as maximum likelihood (ML) or maximum a posteriori probability…

Disordered Systems and Neural Networks · Physics 2020-07-09 ACC Coolen , M Sheikh , A Mozeika , F Aguirre-Lopez , F Antenucci

Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…

Machine Learning · Statistics 2022-02-04 Alexis Ayme , Claire Boyer , Aymeric Dieuleveut , Erwan Scornet

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…

Statistics Theory · Mathematics 2016-01-27 David Dereudre , Frédéric Lavancier

This paper deals with multivariate Gaussian models for which the covariance matrix is a Kronecker product of two matrices. We consider maximum likelihood estimation of the model parameters, in particular of the covariance matrix. There is…

Statistics Theory · Mathematics 2014-10-09 Beata Roś , Fetsje Bijma , Jan C. de Munck , Mathisca C. M. de Gunst

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

Methodology · Statistics 2023-04-21 Ioannis Kalogridis , Gerda Claeskens , Stefan Van Aelst