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A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with…
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…
This article focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas…
Quantitative characterization of disease progression using longitudinal data can provide long-term predictions for the pathological stages of individuals. This work studies the robust modeling of Alzheimer's disease progression using…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
Multimodal data analysis can lead to more accurate diagnoses of brain disorders due to the complementary information that each modality adds. However, a major challenge of using multimodal datasets in the neuroimaging field is incomplete…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocs of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
The additive partially linear model (APLM) combines the flexibility of nonparametric regression with the parsimony of regression models, and has been widely used as a popular tool in multivariate nonparametric regression to alleviate the…
Partial Least Squares (PLS) regression emerged as an alternative to ordinary least squares for addressing multicollinearity in a wide range of scientific applications. As multidimensional tensor data is becoming more widespread, tensor…
In time series analysis, when fitting an autoregressive model, one must solve a Toeplitz ordinary least squares problem numerous times to find an appropriate model, which can severely affect computational times with large data sets. Two…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
We propose a versatile framework for survival analysis that combines advanced concepts from statistics with deep learning. The presented framework is based on piecewise exponential models and thereby supports various survival tasks, such as…
Longitudinal fMRI datasets hold great promise for the study of neurodegenerative diseases, but realizing their potential depends on extracting accurate fMRI-based brain measures in individuals over time. This is especially true for rare,…
Alzheimer's disease is a debilitating disorder marked by a decline in cognitive function. Timely identification of the disease is essential for the development of personalized treatment strategies that aim to mitigate its progression. The…
Latent structure methods, specifically linear continuous latent structure methods, are a type of fundamental statistical learning strategy. They are widely used for dimension reduction, regression and prediction, in the fields of…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
Nonparametric partitioning-based least squares regression is an important tool in empirical work. Common examples include regressions based on splines, wavelets, and piecewise polynomials. This article discusses the main methodological and…