Related papers: Weak separation in mixture models and implications…
Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…
This paper studies treatment effect models in which individuals are classified into unobserved groups based on heterogeneous treatment rules. Using a finite mixture approach, we propose a marginal treatment effect (MTE) framework in which…
There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…
Mixed membership models are an extension of finite mixture models, where each observation can partially belong to more than one mixture component. A probabilistic framework for mixed membership models of high-dimensional continuous data is…
Singularities of a statistical model are the elements of the model's parameter space which make the corresponding Fisher information matrix degenerate. These are the points for which estimation techniques such as the maximum likelihood…
This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the…
Confounding can lead to spurious associations. Typically, one must observe confounders in order to adjust for them, but in high-dimensional settings, recent research has shown that it becomes possible to adjust even for unobserved…
Model selection, via penalized likelihood type criteria, is a standard task in many statistical inference and machine learning problems. Progress has led to deriving criteria with asymptotic consistency results and an increasing emphasis on…
The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete…
We provide a theoretical treatment of over-specified Gaussian mixtures of experts with covariate-free gating networks. We establish the convergence rates of the maximum likelihood estimation (MLE) for these models. Our proof technique is…
Social and economic studies are often implemented as complex survey designs. For example, multistage, unequal probability sampling designs utilized by federal statistical agencies are typically constructed to maximize the efficiency of the…
The nonparametric maximum likelihood estimator (NPMLE) in monotone binary regression models is studied when the impact of the features on the labels is weak. Here, weakness is colloquially understood as "close to flatness" of the…
The predictive capabilities of machine learning (ML) models used in materials discovery are typically measured using simple statistics such as the root-mean-square error (RMSE) or the coefficient of determination ($r^2$) between…
The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…
We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i.i.d. samples are known to have lower accuracy than the classical $n^{- \frac{1}{2}}$ error. We investigate…
Model averaging (MA) and ensembling play a crucial role in statistical and machine learning practice. When multiple candidate models are considered, MA techniques can be used to weight and combine them, often resulting in improved…
Penalized generalized estimating equations (PGEE) stabilize point estimation for longitudinal binary data under near-separation, but inference still depends on how the sandwich variance is corrected. Existing corrections for PGEE can…
Finite mixtures of multivariate normal distributions have been widely used in empirical applications in diverse fields such as statistical genetics and statistical finance. Testing the number of components in multivariate normal mixture…
Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…
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…