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We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form $f_0=\exp\varphi_0$ where $\varphi_0$ is a concave function on $\mathbb{R}$. The pointwise…

Statistics Theory · Mathematics 2023-04-17 Fadoua Balabdaoui , Kaspar Rufibach , Jon A. Wellner

Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximum likelihood (ML) estimators when likelihood functions are more difficult to manipulate than their marginal and conditional components. Furthermore, MPL estimators…

Methodology · Statistics 2017-08-30 Hien D. Nguyen

We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable based on censored data. More specifically, the event time is subject to current status censoring and the continuous mark…

Statistics Theory · Mathematics 2011-09-07 Piet Groeneboom , Geurt Jongbloed , Birgit Witte

We present a review of some recent results on estimation of location parameter for several models of observations with cusp-type singularity at the change point. We suppose that the cusp-type models fit better to the real phenomena…

Statistics Theory · Mathematics 2017-11-13 S. Dachian , N. Kordzakhia , Yu. A. Kutoyants , A. Novikov

We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…

Statistics Theory · Mathematics 2022-05-04 Han Yuecai , Zhang Dingwen

We consider a discrete-time random walk where the random increment at time step $t$ depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition…

Statistical Mechanics · Physics 2009-11-10 Gunter M. Schütz , Steffen Trimper

While the ordinary least squares estimator (OLSE) is still the most used estimator in linear regression models, other estimators can be more efficient when the error distribution is not Gaussian. In this paper, our goal is to evaluate this…

Statistics Theory · Mathematics 2025-10-31 Fadoua Balabdaoui , Justine Leclerc

We study multivariate Gaussian statistical models whose maximum likelihood estimator (MLE) is a rational function of the observed data. We establish a one-to-one correspondence between such models and the solutions to a nonlinear…

Algebraic Geometry · Mathematics 2025-09-04 Carlos Améndola , Lukas Gustafsson , Kathlén Kohn , Orlando Marigliano , Anna Seigal

We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well as incorrect…

Machine Learning · Computer Science 2022-02-09 Deebul S. Nair , Nico Hochgeschwender , Miguel A. Olivares-Mendez

The parameter estimation of unnormalized models is a challenging problem. The maximum likelihood estimation (MLE) is computationally infeasible for these models since normalizing constants are not explicitly calculated. Although some…

Machine Learning · Statistics 2020-06-09 Masatoshi Uehara , Takafumi Kanamori , Takashi Takenouchi , Takeru Matsuda

In this letter, we revisit the problem of maximum likelihood estimation (MLE) of parameters of Gaussian Mixture Model (GMM) and show a new derivation for its parameters. The new derivation, unlike the classical approach employing the…

Signal Processing · Electrical Eng. & Systems 2020-01-10 Nitesh Sahu , Prabhu Babu

Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used…

Methodology · Statistics 2021-03-02 Zhong Guan

The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function,…

Probability · Mathematics 2018-12-27 Yuliya Mishura , Kostiantyn Ralchenko , Sergiy Shklyar

We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on a finite time interval. Under suitable regularity…

Statistics Theory · Mathematics 2014-08-25 Debashis Paul , Jie Peng , Prabir Burman

We consider trawl processes, which are stationary and infinitely divisible stochastic processes and can describe a wide range of statistical properties, such as heavy tails and long memory. In this paper, we develop the first…

Methodology · Statistics 2023-08-31 Dan Leonte , Almut E. D. Veraart

Use of machine learning to estimate nuisance functions (e.g. outcomes models, propensity score models) in estimators used in causal inference is increasingly common, as it can mitigate bias due to model misspecification. However, it can be…

Methodology · Statistics 2025-07-17 Rachael K. Ross , Lina M. Montoya , Dana E. Goin , Ivan Diaz , Audrey Renson

The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…

Data Analysis, Statistics and Probability · Physics 2009-11-13 D. Kleinhans , R. Friedrich

We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…

Statistical Mechanics · Physics 2010-06-18 L. Turban

In recent years, addressing the challenges posed by massive datasets has led researchers to explore aggregated data, particularly leveraging interval-valued data, akin to traditional symbolic data analysis. While much recent research, with…

Methodology · Statistics 2024-05-13 Ali Sadeghkhani , Abdolnasser Sadeghkhani

Maximum likelihood estimation (MLE) and heuristic predictive estimation (HPE) are two widely used approaches in industrial uncertainty analysis. We review them from the point of view of decision theory, using Bayesian inference as a gold…

Applications · Statistics 2010-09-23 Merlin Keller , Eric Parent , Alberto Pasanisi