Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits

Estimation for the bivariate quantile varying coefficient model with application to diffusion tensor imaging data analysis

Despite interest in the joint modeling of multiple functional responses such as diffusion properties in neuroimaging, robust statistical methods appropriate for this task are lacking. To address this need, we propose a varying coefficient quantile regression model able to handle bivariate functional responses. Our work supports innovative insights into biomedical data by modeling the joint distribution of functional variables over their domains and across clinical covariates. We propose an estimation procedure based on the alternating direction method of multipliers and propagation separation algorithms to estimate varying coefficients using a B-spline basis and an $L_2$ smoothness penalty that encourages interpretability. A simulation study and an application to a real-world neurodevelopmental data set demonstrates the performance of our model and the insights provided by modeling functional fractional anisotropy and mean diffusivity jointly and their association with gestational age and sex.

Analysis of CO2 emissions and energy consumption by sources in MENA countries: evidence from quantile regressions

The development of economies and energy usage can significantly impact the carbon dioxide (CO₂) emissions in the Middle East and North Africa (MENA) countries. Therefore, this study aims to analyze the factors that determine CO₂ emissions in MENA under the environmental Kuznets curve (EKC) framework by applying novel quantile techniques on data for CO₂ emissions, real income, renewable and non-renewable energy consumption, and urbanization over the period from 1990 to 2015. The results from the estimations suggest that renewable energy consumption significantly reduces the level of emissions; furthermore, its impact increases with higher quantiles. In addition, non-renewable energy consumption increases CO₂ emissions, while its magnitude decreases with higher quantiles. The empirical results also confirm the validity of EKC hypothesis for the panel of MENA economies. Policymakers in the region should implement policies and regulations to promote the adoption and use of renewable energy to mitigate carbon emissions.

Stable Anatomy Detection in Multimodal Imaging Through Sparse Group Regularization: A Comparative Study of Iron Accumulation in the Aging Brain

Multimodal neuroimaging provides a rich source of data for identifying brain regions associated with disease progression and aging. However, present studies still typically analyze modalities separately or aggregate voxel-wise measurements and analyses to the structural level, thus reducing statistical power. As a central example, previous works have used two quantitative MRI parameters-R2* and quantitative susceptibility (QS)-to study changes in iron associated with aging in healthy and multiple sclerosis subjects, but failed to simultaneously account for both. In this article, we propose a unified framework that combines information from multiple imaging modalities and regularizes estimates for increased interpretability, generalizability, and stability. Our work focuses on joint region detection problems where overlap between effect supports across modalities is encouraged but not strictly enforced. To achieve this, we combine L ₁ (lasso), total variation (TV), and L ₂ group lasso penalties. While the TV penalty encourages geometric regularization by controlling estimate variability and support boundary geometry, the group lasso penalty accounts for similarities in the support between imaging modalities. We address the computational difficulty in this regularization scheme with an alternating direction method of multipliers (ADMM) optimizer. In a neuroimaging application, we compare our method against independent sparse and joint sparse models using a dataset of R2* and QS maps derived from MRI scans of 113 healthy controls: our method produces clinically-interpretable regions where specific iron changes are associated with healthy aging. Together with results across multiple simulation studies, we conclude that our approach identifies regions that are more strongly associated with the variable of interest (e.g., age), more accurate, and more stable with respect to training data variability. This work makes progress toward a stable and interpretable multimodal imaging analysis framework for studying disease-related changes in brain structure and can be extended for classification and disease prediction tasks.

Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions

Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study.