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Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…

Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…

We introduce mixed model trace regression (MMTR), a mixed model linear regression extension for scalar responses and high-dimensional matrix-valued covariates. MMTR's fixed effects component is equivalent to trace regression, with an…

Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…

The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…

Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that…

This article proposes a novel estimator for regression coefficients in clustered data that explicitly accounts for within-cluster dependence. We study the asymptotic properties of the proposed estimator under both finite and infinite…

It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data…

Overparameterization in deep learning is powerful: Very large models fit the training data perfectly and yet often generalize well. This realization brought back the study of linear models for regression, including ordinary least squares…

Missing covariate data commonly occur in epidemiological and clinical research, and are often dealt with using multiple imputation (MI). Imputation of partially observed covariates is complicated if the substantive model is non-linear (e.g.…

Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the…

This paper deals with the problem of covariance stabilization for a class of linear stochastic discrete-time systems in the Stochastic Model Predictive Control (SMPC) framework. The considered systems are affected by independent and…

Linear minimum mean square error (LMMSE) estimation is often ill-conditioned, suggesting that unconstrained minimization of the mean square error is an inadequate approach to filter design. To address this, we first develop a unifying…

Generalized linear models are a popular tool in applied statistics, with their maximum likelihood estimators enjoying asymptotic Gaussianity and efficiency. As all models are wrong, it is desirable to understand these estimators' behaviours…

For data with high-dimensional covariates but small to moderate sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of…

We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of…

Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…

Stepped wedge designs (SWDs) are increasingly used to evaluate longitudinal cluster-level interventions but pose substantial challenges for valid inference. Because crossover times are randomized, intervention effects are intrinsically…

We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying…

In this self-contained chapter, we revisit a fundamental problem of multivariate statistics: estimating covariance matrices from finitely many independent samples. Based on massive Multiple-Input Multiple-Output (MIMO) systems we illustrate…