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We study the maximum smoothed likelihood estimator (MSLE) for interval censoring, case 2, in the so-called separated case. Characterizations in terms of convex duality conditions are given and strong consistency is proved. Moreover, we show…

Statistics Theory · Mathematics 2014-10-16 Piet Groeneboom

In this article, we present the maximum weighted likelihood estimator (MWLE) for robust estimations of heavy-tail finite mixture models (FMM). This is motivated by the complex distributional phenomena of insurance claim severity data, where…

Methodology · Statistics 2021-08-04 Tsz Chai Fung

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…

Statistics Theory · Mathematics 2016-04-19 Andreas Anastasiou , Christophe Ley

We study the problem of maximum likelihood estimation given one data sample ($n=1$) over Brownian Motion Tree Models (BMTMs), a class of Gaussian models on trees. BMTMs are often used as a null model in phylogenetics, where the one-sample…

Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…

Probability · Mathematics 2023-01-16 Xinpeng Li , Yue Liu , Jiaquan Lu

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

Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…

Statistics Theory · Mathematics 2022-06-08 Pragya Sur , Emmanuel J. Candes

We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…

Machine Learning · Computer Science 2023-10-24 Jian-Feng Cai , José Vinícius de M. Cardoso , Daniel P. Palomar , Jiaxi Ying

In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three…

Representation Theory · Mathematics 2020-07-21 Harm Derksen , Visu Makam

Consider the mean-field spin models where the Gibbs measure of each configuration depends only on its magnetization. Based on the Stein and Laplace methods, we give a new and short proof for the scaling limit theorems with convergence rate…

Probability · Mathematics 2025-03-18 Van Hao Can , Adrian Röllin

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

Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution that best explain the observed data. In the context of text generation, MLE is often used to train generative language…

Computation and Language · Computer Science 2023-10-27 Chenze Shao , Zhengrui Ma , Min Zhang , Yang Feng

Consider an $(L,1)$ random walk in an i.i.d. random environment, whose environment involves certain parameter. We get the maximum likelihood estimator(MLE) of the environment parameter which can be written as functionals of a multitype…

Statistics Theory · Mathematics 2018-08-31 Hua-Ming Wang , Meijuan Zhang

Asymptotic efficiency of targeted maximum likelihood estimators (TMLE) of target features of the data distribution relies on a a second order remainder being asymptotically negligible. In previous work we proposed a nonparametric MLE termed…

Statistics Theory · Mathematics 2021-07-02 Mark van der Laan , Zeyi Wang , Lars van der Laan

We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…

Populations and Evolution · Quantitative Biology 2007-08-17 Mike Steel , Allen Rodrigo

The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…

Combinatorics · Mathematics 2015-09-17 Elizabeth Gross , Seth Sullivant

Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system…

Machine Learning · Statistics 2020-03-11 Junghyo Jo , Danh-Tai Hoang , Vipul Periwal

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…

Signal Processing · Electrical Eng. & Systems 2025-05-13 Augusto Aubry , Prabhu Babu , Antonio De Maio , Massimo Rosamilia

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

We consider hidden Markov models indexed by a binary tree where the hidden state space is a general metric space. We study the maximum likelihood estimator (MLE) of the model parameters based only on the observed variables. In both…

Probability · Mathematics 2025-08-20 Julien Weibel