Related papers: A New Model Variance Estimator for an Area Level S…
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…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…
We consider a linear regression model with a spatially correlated error term on a lattice. When estimating coefficients in the linear regression model, the generalized least squares estimator (GLSE) is used if the covariance structures are…
Sample surveys are widely used to obtain information about totals, means, medians, and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific…
The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use…
Accurate estimates of subnational health and demographic indicators are critical for informing health policy decisions. Many countries collect relevant data using complex household surveys, but when data are limited, direct survey weighted…
In real applications of small area estimation, one often encounters data with positive response values. The use of a parametric transformation for positive response values in the Fay-Herriot model is proposed for such a case. An…
We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…
We propose a variational autoencoder (VAE) approach for parameter estimation in nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs) using longitudinal data from multiple subjects. In moderate dimensions,…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
Small area estimation (SAE) produces estimates of population parameters for geographic and demographic subgroups with limited sample sizes. Such estimates are critical for informing policy decisions, ranging from poverty mapping to social…
In modern statistics, interests shift from pursuing the uniformly minimum variance unbiased estimator to reducing mean squared error (MSE) or residual squared error. Shrinkage based estimation and regression methods offer better prediction…
In this paper, the line spectral estimation (LSE) problem with multiple measurement vectors (MMVs) is studied utilizing the Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) method, we develop…
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…
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…
Understanding the nuanced performance of machine learning models is essential for responsible deployment, especially in high-stakes domains like healthcare and finance. This paper introduces a novel framework, Conformalized Exceptional…
We develop an envelope model for joint mean and covariance regression in the large $p$, small $n$ setting. In contrast to existing envelope methods, which improve mean estimates by incorporating estimates of the covariance structure, we…
Subnational monitoring of public health often relies on household surveys where data are sparse at the desired spatial resolution. Small area estimation (SAE) methods address this challenge by borrowing strength across areas and…
As regression is a widely studied problem, many methods have been proposed to solve it, each of them often requiring setting different hyper-parameters. Therefore, selecting the proper method for a given application may be very difficult…
State-space models have been used in many applications, including econometrics, engineering, medical research, etc. The maximum likelihood estimation (MLE) of the static parameter of general state-space models is not straightforward because…