Related papers: Likelihood Correspondence of Toric Statistical Mod…

We show that there is an intimate connection between the theory of nonparametric (smoothed) maximum likelihood estimators for certain inverse problems and integral equations. This is illustrated by estimators for interval censoring and…

Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying…

We introduce a general covariate-assisted statistical ranking model within the Plackett--Luce framework. Unlike previous studies focusing on individual effects with fixed covariates, our model allows covariates to vary across comparisons.…

Maximum likelihood estimation (MLE) methods are widely used for evolutionary tree. As evolutionary tree is not a smooth parameter, the consistency of its MLE has been a topic of debate. It has been noted without proof that the classical…

Phylogenetic models have polynomial parametrization maps. For symmetric group-based models, Matsen studied the polynomial inequalities that characterize the joint probabilities in the image of these parametrizations. We employ this…

The key point limits to define the {\it statistical model} describing the data distribution. Hence, it turns out that the characteristics related to the so-called. Inverse Tully-Fisher relation and the Direct relation are maximum likelyhood…

As is the case for many curved exponential families, the computation of maximum likelihood estimates in a multivariate normal model with a Kronecker covariance structure is typically carried out with an iterative algorithm, specifically, a…

In this article, we present the maximum weighted likelihood estimator (MWLE) for robust estimations of heavy-tail finite mixture models (FMM). This is motivated by the complex distributional phenomena of insurance claim severity data, where…

The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…

Completion problems, of recovering a point from a set of observed coordinates, are abundant in applications to image reconstruction, phylogenetics, and data science. We consider a completion problem coming from algebraic statistics: to…

In a finite mixture of location-scale distributions maximum likelihood estimator does not exist because of the unboundedness of the likelihood function when the scale parameter of some mixture component approaches zero. In order to study…

Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and…

Monte Carlo maximum likelihood (MCML) provides an elegant approach to find maximum likelihood estimators (MLEs) for latent variable models. However, MCML algorithms are computationally expensive when the latent variables are…

Suppose we are given observations, where each observation is drawn independently from one of $k$ known distributions. The goal is to match each observation to the distribution from which it was drawn. We observe that the maximum likelihood…

Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent…

The traditional maximum likelihood estimator (MLE) is often of limited use in complex high-dimensional data due to the intractability of the underlying likelihood function. Maximum composite likelihood estimation (McLE) avoids full…

We study the problem of maximizing information divergence from a new perspective using logarithmic Voronoi polytopes. We show that for linear models, the maximum is always achieved at the boundary of the probability simplex. For toric…

This paper presents a tractable sufficient condition for the consistency of maximum likelihood estimators (MLEs) in partially observed diffusion models, stated in terms of stationary distribution of the associated fully observed diffusion,…

We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and…

The exact maximum likelihood estimate (MLE) provides a test statistic for the unit root test that is more powerful \citep[p. 577]{Fuller96} than the usual least squares approach. In this paper a new derivation is given for the asymptotic…