Related papers: Developments in Maximum Likelihood Unit Root Tests

In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to…

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…

The classical likelihood ratio test (LRT) based on the asymptotic chi-squared distribution of the log likelihood is one of the fundamental tools of statistical inference. A recent universal LRT approach based on sample splitting provides…

We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently…

Maximum pseudo-likelihood (MPL) is a semiparametric estimation method often used to obtain the dependence parameters in copula models from data. It has been shown that despite being consistent, and in some cases efficient, MPL estimation…

Several recently developed methods have the potential to harness machine learning in the pursuit of target quantities inspired by causal inference, including inverse weighting, doubly robust estimating equations and substitution estimators…

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…

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the…

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…

Unlike the ordinary least-squares (OLS) estimator for the linear model, a ridge regression linear model provides coefficient estimates via shrinkage, usually with improved mean-square and prediction error. This is true especially when the…

State-space models have been used in many applications, including econometrics, engineering, medical research, etc. The maximum likelihood estimation (MLE) of the static parameter of general state-space models is not straightforward because…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

There have been many applications of deep neural networks to detector calibrations and a growing number of studies that propose deep generative models as automated fast detector simulators. We show that these two tasks can be unified by…

The ability to rigorously estimate the failure rates of large language models (LLMs) is a prerequisite for their safe deployment. Currently, however, practitioners often face a tradeoff between expensive human gold standards and potentially…

The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of…

The construction of computer models (mathematical models implemented in computer codes), with respect to observed phenomena, is usually undertaken by building different variants depending on modeller sensibility, and choosing the one…

Scientific machine learning (SciML) is a field of increasing interest in several different application fields. In an optimization context, SciML-based tools have enabled the development of more efficient optimization methods. However,…

Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…

We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum…

Since the dawn of response surface methodology, it has been recommended that designs include replicate points, so that pure error estimates of variance can be obtained and used to provide unbiased estimated standard errors of the effects of…