Related papers: Empirical Best Linear Unbiased Predictors in Multi…
We study the excess mean square error (EMSE) above the minimum mean square error (MMSE) in large linear systems where the posterior mean estimator (PME) is evaluated with a postulated prior that differs from the true prior of the input…
As the maximum likelihood method is the most commonly used method for parameters estimation being unbiased, consistent, efficient, and asymptotically normal, MLE is used to fit the new distribution (MBUW). But in small to moderate sample…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
National statistical institutes in many countries are now mandated to produce reliable statistics for important variables such as population, income, unemployment, health outcomes, etc. for small areas, defined by geography and/or…
The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
Health disparity research often evaluates health outcomes across demographic subgroups. Multilevel regression and poststratification (MRP) is a popular approach for small subgroup estimation due to its ability to stabilize estimates by…
Machine learning models have exhibited exceptional results in various domains. The most prevalent approach for learning is the empirical risk minimizer (ERM), which adapts the model's weights to reduce the loss on a training set and…
For classical estimation with an underlying linear model the best linear unbiased estimator (BLUE) is usually utilized for estimating the deterministic but unknown parameter vector. In the case of real valued parameter vectors but complex…
We study empirical Bayes (EB) predictive density estimation in linear mixed models (LMMs) with large number of units, which induce a high dimensional random effects space. Focusing on Kullback Leibler (KL) risk minimization, we develop a…
This work concerns the estimation of multidimensional nonlinear regression models using multilayer perceptrons (MLPs). The main problem with such models is that we need to know the covariance matrix of the noise to get an optimal estimator.…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
Discriminative latent-variable models are typically learned using EM or gradient-based optimization, which suffer from local optima. In this paper, we develop a new computationally efficient and provably consistent estimator for a mixture…
Multilevel estimators aim at reducing the variance of Monte Carlo statistical estimators, by combining samples generated with simulators of different costs and accuracies. In particular, the recent work of Schaden and Ullmann (2020) on the…
Statistical agencies are often asked to produce small area estimates (SAEs) for positively skewed variables. When domain sample sizes are too small to support direct estimators, effects of skewness of the response variable can be large. As…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
We study a regression problem where for some part of the data we observe both the label variable ($Y$) and the predictors (${\bf X}$), while for other part of the data only the predictors are given. Such a problem arises, for example, when…
Unbiased estimation for parameters of maximal distribution is a very fundamental problem in the statistical theory of sublinear expectation. In this paper, we proved that the maximum estimator is the largest unbiased estimator for the upper…
In the framework of mutually unbiased bases (MUBs), a measurement in one basis gives \emph{no information} about the outcomes of measurements in another basis. Here, we relax the no-information condition by allowing the $d$ outcomes to be…
We study Off-Policy Evaluation (OPE) in contextual bandit settings with large action spaces. The benchmark estimators suffer from severe bias and variance tradeoffs. Parametric approaches suffer from bias due to difficulty specifying the…