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High-dimensional linear regression is a fundamental tool in modern statistics, particularly when the number of predictors exceeds the sample size. The classical Lasso, which relies on the squared loss, performs well under Gaussian noise…
We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to…
Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between…
In this work, we propose a deep learning-based method to perform semiparametric regression analysis for spatially dependent data. To be specific, we use a sparsely connected deep neural network with rectified linear unit (ReLU) activation…
Various frameworks have been proposed to predict mechanical system responses by combining data from different fidelities for design optimization and uncertainty quantification as reviewed by Fern\'andez-Godino et al. and Peherstorfer et…
This paper investigates a partially linear spatial autoregressive panel data model that incorporates fixed effects, constant and time-varying regression coefficients, and a time-varying spatial lag coefficient. A two-stage least squares…
We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology…
Forward regression is a classical and effective tool for variable screening in ultra-high dimensional linear models, but its standard projection-based implementation can be computationally costly and numerically unstable when predictors are…
We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a…
This paper introduces an explicit residual-based a posteriori error analysis for the symmetric mixed finite element method in linear elasticity after Arnold-Winther with pointwise symmetric and H(div)-conforming stress approximation.…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
We focus on nonlinear Function-on-Scalar regression, where the predictors are scalar variables, and the responses are functional data. Most existing studies approximate the hidden nonlinear relationships using linear combinations of basis…
Hierarchical spatial models are very flexible and popular for a vast array of applications in areas such as ecology, social science, public health, and atmospheric science. It is common to carry out Bayesian inference for these models via…
In small area estimation, it is a smart strategy to rely on data measured over time. However, linear mixed models struggle to properly capture time dependencies when the number of lags is large. Given the lack of published studies…
In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…
Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models $-$ i.e., low-rank plus diagonal covariance structures $-$ offer a powerful framework…
The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…
Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…
In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…
Recent technological developments have enabled us to collect complex and high-dimensional data in many scientific fields, such as population health, meteorology, econometrics, geology, and psychology. It is common to encounter such datasets…