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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,…

Econometrics · Economics 2019-08-13 Michael Griebel , Florian Heiss , Jens Oettershagen , Constantin Weiser

Given a statistical model, the maximum likelihood degree is the number of complex solutions to the likelihood equations for generic data. We consider discrete algebraic statistical models and study the solutions to the likelihood equations…

Algebraic Geometry · Mathematics 2014-05-06 Elizabeth Gross , Jose Israel Rodriguez

In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the…

Methodology · Statistics 2022-07-14 Thobeka Nombebe , James Allison , Leonard Santana , Jaco Visagie

We consider discrete default intensity based and logit type reduced form models for conditional default probabilities for corporate loans where we develop simple closed form approximations to the maximum likelihood estimator (MLE) when the…

Econometrics · Economics 2020-01-01 Anand Deo , Sandeep Juneja

We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…

Statistics Theory · Mathematics 2010-01-13 Piet Groeneboom , Geurt Jongbloed , Birgit I. Witte

Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements…

Methodology · Statistics 2014-09-29 Jiantao Jiao , Kartik Venkat , Yanjun Han , Tsachy Weissman

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…

Statistics Theory · Mathematics 2012-07-24 Stephen E. Fienberg , Alessandro Rinaldo

The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…

Methodology · Statistics 2025-04-16 Pedro L. Ramos , Eduardo Ramos , Francisco A. Rodrigues , Francisco Louzada

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…

We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…

Probability · Mathematics 2021-02-23 Krzysztof Bogdan , Michał Bosy , Tomasz Skalski

We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…

Statistics Theory · Mathematics 2019-02-13 Karl Oskar Ekvall , Galin L. Jones

In this paper, we propose and investigate closed-form point estimators for a weighted exponential family. We also develop a bias-reduced version of these proposed closed-form estimators through bootstrap methods. Estimators are assessed…

Methodology · Statistics 2024-05-28 Roberto Vila , Eduardo Nakano , Helton Saulo

In this paper, novel closed-form point estimators of the beta distribution are proposed and investigated. The first estimators are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient…

Statistics Theory · Mathematics 2022-10-12 Piao Chen , Xun Xiao

Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…

Optimization and Control · Mathematics 2018-01-19 Koulik Khamaru , Rahul Mazumder

The parameters of the log-logistic distribution are generally estimated based on classical methods such as maximum likelihood estimation, whereas these methods usually result in severe biased estimates when the data contain outliers. In…

Methodology · Statistics 2022-09-16 Zhuanzhuan Ma , Min Wang , Chanseok Park

In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…

Statistics Theory · Mathematics 2018-01-12 Dragi Anevski , Richard D. Gill , Stefan Zohren

It is a well-known issue that in Item Response Theory models there is no closed-form for the maximum likelihood estimators of the item parameters. Parameter estimation is therefore typically achieved by means of numerical methods like…

Methodology · Statistics 2024-11-28 Stefano Noventa , Roberto Faleh , Augustin Kelava

A hidden Markov model with trends is a hidden Markov model whose emission distributions are translated by a trend that depends on the current hidden state and on the current time. Contrary to standard hidden Markov models, such processes…

Statistics Theory · Mathematics 2021-12-17 Luc Lehéricy , Augustin Touron

Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum…

Methodology · Statistics 2016-01-06 Jiahe Lin , Sumanta Basu , Moulinath Banerjee , George Michailidis

In many complex statistical models maximum likelihood estimators cannot be calculated. In the paper we solve this problem using Markov chain Monte Carlo approximation of the true likelihood. In the main result we prove asymptotic normality…

Statistics Theory · Mathematics 2018-08-09 Błażej Miasojedow , Wojciech Niemiro , Wojciech Rejchel