Related papers: CWCU LMMSE Estimation: Prerequisites and Propertie…
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…
Despite the simplicity and intuitive interpretation of Minimum Mean Squared Error (MMSE) estimators, their effectiveness in certain scenarios is questionable. Indeed, minimizing squared errors on average does not provide any form of…
This paper studies the minimum mean squared error (MMSE) of estimating $\mathbf{X} \in \mathbb{R}^d$ from the noisy observation $\mathbf{Y} \in \mathbb{R}^k$, under the assumption that the noise (i.e., $\mathbf{Y}|\mathbf{X}$) is a member…
The minimum mean square error of the estimation of a non Gaussian signal where observed from an additive white Gaussian noise channel's output, is analyzed. First, a quite general time-continuous channel model is assumed for which the…
The Rasch model is widely used for item response analysis in applications ranging from recommender systems to psychology, education, and finance. While a number of estimators have been proposed for the Rasch model over the last decades, the…
This note examines the behavior of generalization capabilities - as defined by out-of-sample mean squared error (MSE) - of Linear Gaussian (with a fixed design matrix) and Linear Least Squares regression. Particularly, we consider a…
This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is…
Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…
Causal inference methods have been applied in various fields where researchers want to estimate treatment effects. In traditional causal inference settings, one assumes that the outcome of a unit does not depend on treatments of other…
In continuation to a recent work on the statistical--mechanical analysis of minimum mean square error (MMSE) estimation in Gaussian noise via its relation to the mutual information (the I-MMSE relation), here we propose a simple and more…
In this paper we have proposed an almost unbiased estimator using known value of some population parameter(s) with known population proportion of an auxiliary variable. A class of estimators is defined which includes [1], [2] and [3]…
The James-Stein estimator's dominance over maximum likelihood in terms of mean square error (MSE) has been one of the most celebrated results in modern statistics, suggesting that biased estimators can systematically outperform unbiased…
A major limitation of machine learning (ML) prediction models is that they recover associational, rather than causal, predictive relationships between variables. In high-stakes automation applications of ML this is problematic, as the model…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…
In this paper, we consider the problem of recovering random graph signals with complex values. For general Bayesian estimation of complex-valued vectors, it is known that the widely-linear minimum mean-squared-error (WLMMSE) estimator can…
We consider estimating a low-dimensional parameter in an estimating equation involving high-dimensional nuisances that depend on the parameter. A central example is the efficient estimating equation for the (local) quantile treatment effect…
In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…
Suppose a linear model y = Hx + n, where inputs x, n are independent Gaussian mixtures. The problem is to design the transfer matrix H so as to minimize the mean square error (MSE) when estimating x from y. This problem has important…
Cosmic Microwave Background (CMB) lensing is a powerful probe of the matter distribution in the Universe. The standard quadratic estimator, which is typically used to measure the lensing signal, is known to be suboptimal for low-noise…
Ultra-reliable underwater acoustic (UWA) communications serve as one of the key enabling technologies for future space-air-ground-underwater integrated networks. However, the reliability of current UWA transmission is still insufficient…