Related papers: Group-Linear Empirical Bayes Estimates for a Heter…
In this manuscript, we investigate the concept of the mean response for a treatment group mean as well as its estimation and prediction for generalized linear models with a subject-wise random effect. Generalized linear models are commonly…
Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean-variance estimation networks can learn this type of uncertainty but…
Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…
Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…
We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result…
We consider two problems of estimation in high-dimensional Gaussian models. The first problem is that of estimating a linear functional of the means of $n$ independent $p$-dimensional Gaussian vectors, under the assumption that most of…
In this paper we propose a semi-parametric Bayesian Generalized Least Squares estimator. In a generic setting where each error is a vector, the parametric Generalized Least Square estimator maintains the assumption that each error vector…
Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…
Regularization in fitting regression models has been a highly active topic of research in the past few decades, but most of the existing methods are designed for particular situations, e.g. for the case of a sparse coefficient vector. We…
We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…
Measurement error data or errors-in-variable data have been collected in many studies. Natural criterion functions are often unavailable for general functional measurement error models due to the lack of information on the distribution of…
We consider batch size selection for a general class of multivariate batch means variance estimators, which are computationally viable for high-dimensional Markov chain Monte Carlo simulations. We derive the asymptotic mean squared error…
This note is concerned with an accurate and computationally efficient variational bayesian treatment of mixed-effects modelling. We focus on group studies, i.e. empirical studies that report multiple measurements acquired in multiple…
The two-level normal hierarchical model has played an important role in statistical theory and applications. In this paper, we first introduce a general adjusted maximum likelihood method for estimating the unknown variance component of the…
We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…
We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The intervals are centered at the usual linear empirical Bayes estimator, but use a critical value accounting for shrinkage. Parametric EBCIs that…
We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function in combining information from multiple sources to improve traditional survey estimates of finite population…
We analyze the problem of estimating a signal from multiple measurements on a $\mbox{group action channel}$ that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel…