Related papers: Random Effects Misspecification and its Consequenc…
We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…
Linear mixed models with large imbalanced crossed random effects structures pose severe computational problems for maximum likelihood estimation and for Bayesian analysis. The costs can grow as fast as $N^{3/2}$ when there are N…
Exact MLE for generalized linear mixed models (GLMMs) is a long-standing problem unsolved until today. The proposed research solves the problem. In this problem, the main difficulty is caused by intractable integrals in the likelihood…
Estimation under model misspecification arises in many signal processing problems, where the assumed observation model deviates from the true data-generating mechanism due to errors or simplifications. The misspecified Cram\'er-Rao bound…
In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no…
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
Recently, applied sciences, including longitudinal and clustered studies in biomedicine require the analysis of ultra-high dimensional linear mixed effects models where we need to select important fixed effect variables from a vast pool of…
The Hausman specification test assesses the random-effects specification by comparing the random-effects estimator with a fixed-effects alternative. This note shows how a recently proposed bias diagnostic for linear mixed models can…
In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…
Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional…
Model misspecification is ubiquitous in data analysis because the data-generating process is often complex and mathematically intractable. Therefore, assessing estimation uncertainty and conducting statistical inference under a possibly…
Linear mixed-effects models have increasingly replaced mixed-model analyses of variance for statistical inference in factorial psycholinguistic experiments. Although LMMs have many advantages over ANOVA, like ANOVAs, setting them up for…
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…
In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common…
Parameter estimation via unbinned maximum likelihood fits is central for many analyses performed in high energy physics. Unbinned maximum likelihood fits using event weights, for example to statistically subtract background contributions…
In industrial experiments, controlling variability is of paramount importance to ensure product quality. Classical regression models for mixture experiments are widely used in industry, however, when the assumption of constant variance is…
We develop and evaluate point and interval estimates for the random effects $\theta_i$, having made observations $y_i|\theta_i\stackrel{\m athit{ind}}{\sim}N[\theta_i,V_i],i=1,...,k$ that follow a two-level Normal hierarchical model.…
We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…
Finetuning large language models on narrowly harmful datasets can cause them to become emergently misaligned, giving stereotypically `evil' responses across diverse unrelated settings. Concerningly, a pre-registered survey of experts failed…