Related papers: Maximum Likelihood Estimation under the Emax Model…
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…
In this paper we consider two generalizations of Lancaster's (Review of Economic Studies, 2002) Modified Maximum Likelihood estimator (MMLE) for the panel AR(1) model with fixed effects, arbitrary initial conditions, and strictly exogenous…
The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…
We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift…
We import the algebro-geometric notion of a complete collineation into the study of maximum likelihood estimation in directed Gaussian graphical models. A complete collineation produces a perturbation of sample data, which we call a…
Reinforcement learning is the method of choice to train models in sampling-based setups with binary outcome feedback, such as navigation, code generation, and mathematical problem solving. In such settings, models implicitly induce a…
The saddlepoint approximation to the likelihood, and its corresponding maximum likelihood estimate (MLE), offer an alternative estimation method when the true likelihood is intractable or computationally expensive. However, maximizing this…
We present a computational motivation for restricted maximum likelihood (REML) estimation in linear mixed models using an expectation--maximization (EM) algorithm. At each iteration, maximum likelihood (ML) and REML solve the same…
Adaptive experimental designs have gained popularity in clinical trials and online experiments. Unlike traditional, fixed experimental designs, adaptive designs can dynamically adjust treatment randomization probabilities and other design…
We revisit the classical problem of deriving convergence rates for the maximum likelihood estimator (MLE) in finite mixture models. The Wasserstein distance has become a standard loss function for the analysis of parameter estimation in…
Longitudinal targeted maximum likelihood estimation (LTMLE) has very rarely been used to estimate dynamic treatment effects in the context of time-dependent confounding affected by prior treatment when faced with long follow-up times,…
The widespread use of generative models has created a feedback loop, in which each generation of models is trained on data partially produced by its predecessors. This process has raised concerns about model collapse: A critical degradation…
Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered…
Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality.…
Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a…
This paper proposes a closed-form optimal estimator based on the theory of estimating functions for a class of linear ARCH models. The estimating function (EF) estimator has the advantage over the widely used maximum likelihood (ML) and…
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to…
The finite Gamma mixture model is often used to describe randomness in income data, insurance data, and data from other applications. The popular likelihood approach, however, does not work for this model because the likelihood function is…
Complex models used to describe biological processes in epidemiology and ecology often have computationally intractable or expensive likelihoods. This poses significant challenges in terms of Bayesian inference but more significantly in the…
When in a full exponential family the maximum likelihood estimate (MLE) does not exist, the MLE may exist in the Barndorff-Nielsen completion of the family. We propose a practical algorithm for finding the MLE in the completion based on…