Related papers: Existence of Firth's modified estimates in binomia…

Logistic regression models for binomial responses are routinely used in statistical practice. However, the maximum likelihood estimate may not exist due to data separability. We address this issue by considering a conjugate prior penalty…

Firth (1993, Biometrika) shows that the maximum Jeffreys' prior penalized likelihood estimator in logistic regression has asymptotic bias decreasing with the square of the number of observations when the number of parameters is fixed, which…

Penalization of the likelihood by Jeffreys' invariant prior, or by a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of…

Firth-type logistic regression has become a standard approach for the analysis of binary outcomes with small samples. Whereas it reduces the bias in maximum likelihood estimates of coefficients, bias towards 1/2 is introduced in the…

Maximum likelihood estimation in logistic regression with mixed effects is known to often result in estimates on the boundary of the parameter space. Such estimates, which include infinite values for fixed effects and singular or infinite…

The widespread use of maximum Jeffreys'-prior penalized likelihood in binomial-response generalized linear models, and in logistic regression, in particular, are supported by the results of Kosmidis and Firth (2021, Biometrika), who show…

We consider a finite mixture of regressions (FMR) model for high-dimensional inhomogeneous data where the number of covariates may be much larger than sample size. We propose an l1-penalized maximum likelihood estimator in an appropriate…

In finite mixtures of location-scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a…

We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…

By exploiting McFadden (1974)'s results on conditional logit estimation, we show that there exists a one-to-one mapping between existence and uniqueness of conditional maximum likelihood estimates of the binary logit model with fixed…

This study focuses on the estimation of the Emax dose-response model, a widely utilized framework in clinical trials, agriculture, and environmental experiments. Existing challenges in obtaining maximum likelihood estimates (MLE) for model…

Separation in logistic regression is a common problem causing failure of the iterative estimation process when finding maximum likelihood estimates. Firth's correction (FC) was proposed as a solution, providing estimates also in presence of…

A fundamental problem with nonlinear models is that maximum likelihood estimates are not guaranteed to exist. Though nonexistence is a well known problem in the binary response model literature, it presents significant challenges for other…

Motivated by recent works on the high-dimensional logistic regression, we establish that the existence of the maximum likelihood estimate exhibits a phase transition for a wide range of generalized linear models with binary outcome and…

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…

In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. Here, we consider a threshold model that all continuous features are discretized into ordinal levels, which further…

This paper extends some prominent statistical results including \emph{Fisher Theorem and Wilks phenomenon} to the penalized maximum likelihood estimation with a quadratic penalization. It appears that sharp expansions for the penalized MLE…

We address the issue of performing inference on the parameters that index a bimodal extension of the Birnbaum-Saunders distribution (BS). We show that maximum likelihood point estimation can be problematic since the standard nonlinear…

Multiple root estimation problems in statistical inference arise in many contexts in the literature. In the context of maximum likelihood estimation, the existence of multiple roots causes uncertainty in the computation of maximum…

A penalized maximum likelihood estimation approach is proposed for discrete-time hidden Markov models where covariates affect the observed responses and serial dependence is considered. The proposed penalized maximum likelihood method…