English
Related papers

Related papers: Maximum Likelihood Estimation for Brownian Motion …

200 papers

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…

Statistics Theory · Mathematics 2011-11-10 Rainer Dahlhaus , Wolfgang Polonik

If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…

Statistics Theory · Mathematics 2012-07-06 Charles J. Geyer

Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We…

Methodology · Statistics 2014-06-03 Iván Díaz , Michael Rosenblum

Current Targeted Maximum Likelihood Estimation (TMLE) methods used to analyze time-to-event data estimate the survival probability for each time point separately, which result in estimates that are not necessarily monotone. In this paper,…

Methodology · Statistics 2019-06-14 Weixin Cai , Mark J. van der Laan

Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular…

Computation · Statistics 2025-08-26 Xiaochen Long , Marek Kimmel

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

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

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…

Statistics Theory · Mathematics 2019-11-01 Nancy Flournoy , Caterina May , Chiara Tommasi

Quantum state tomography (QST) is typically performed from a frequentist viewpoint using maximum likelihood estimation (MLE) which seeks to find the best plausible state consistent with the data by maximizing a likelihood function /…

Quantum Physics · Physics 2022-12-22 Daniel J. Lum , Yaakov Weinstein

We consider a one dimensional sub-ballistic random walk evolving in a parametric i.i.d. random environment. We study the asymptotic properties of the maximum likelihood estimator (MLE) of the parameter based on a single observation of the…

Probability · Mathematics 2014-05-13 Mikael Falconnet , Dasha Loukianova , Arnaud Gloter

We consider drift parameter estimation in a model driven by the sum of two independent fractional Brownian motions with different Hurst indices. Although the maximum likelihood estimator (MLE) for this model is known theoretically, its…

Probability · Mathematics 2026-03-06 Yuliya Mishura , Kostiantyn Ralchenko , Mykyta Yakovliev

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

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 estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…

Machine Learning · Computer Science 2024-06-05 Jen Ning Lim , Juan Kuntz , Samuel Power , Adam M. Johansen

Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is…

Statistics Theory · Mathematics 2011-03-10 Randal Douc , Eric Moulines , Jimmy Olsson , Ramon van Handel

We can directly sample from the conditional distribution of any log-affine model. The algorithm is a Markov chain on a bounded integer lattice, and its transition probability is the ratio of the UMVUE (uniformly minimum variance unbiased…

Statistics Theory · Mathematics 2025-11-26 Shuhei Mano

The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…

Data Analysis, Statistics and Probability · Physics 2018-12-03 Anthony Vella

We study the consistency and optimality of the maximum marginal likelihood estimate (MMLE) in the hyperparameter inference for large-degree-of-freedom models. We perform main analyses within the exponential family, where the natural…

Statistics Theory · Mathematics 2022-05-27 Dye SK Sato , Yukitoshi Fukahata

Maximum likelihood (ML) estimation is widely used in statistics. The h-likelihood has been proposed as an extension of Fisher's likelihood to statistical models including unobserved latent variables of recent interest. Its advantage is that…

Methodology · Statistics 2022-07-21 Jeongseop Han , Youngjo Lee , Jae Kwang Kim

We consider the branch-length estimation problem on a bifurcating tree: a character evolves along the edges of a binary tree according to a two-state symmetric Markov process, and we seek to recover the edge transition probabilities from…

Computation · Statistics 2025-07-30 David Clancy , Hanbaek Lyu , Sebastien Roch