ABSTRACT Identifying causal variants within genome‐wide association study loci is challenging due to linkage disequilibrium, multi‐signal architectures, and the need for calibrated uncertainty at a large scale. We formulate fine‐mapping as Bayesian variable selection with binary inclusion indicators and propose a variational EM algorithm that learns feature‐specific prior inclusion probabilities via empirical Bayes (EmpBVS). Our E‐step delivers closed‐form updates for the variational Gaussian factor on effects and the noise precision, while the M‐step updates per‐SNP inclusion priors by maximizing the lower bound of marginal data likelihood. Irrelevant SNPs are shrunk out automatically as their weights contract to zero, yielding threshold‐free selection. We establish a computational sparsity result showing geometric decay of null inclusion weights across iterations, and statistical consistency, where posterior mass concentrates on the true model and variational means consistently recover effect sizes. Simulations and comparative experiments demonstrate accurate posterior inclusion probabilities and credible sets with competitive runtime. Our framework thus preserves automatic relevance learning while providing discrete selections and rigorous guarantees tailored to genetic fine‐mapping.

ABSTRACT This paper introduces a new semiparametric spatial regression model with unknown forcing terms (SSRUT) in the prior information of the nonparametric function for spatial anisotropic data. The estimators are obtained by the proposed penalized least squares method which incorporates partial differential equation (PDE) penalization with mixed finite elements. In particular, the unknown coefficient functions in PDE which capture the spatial anisotropy, are chosen by our developed penalized spatial local least squares method. The corresponding implementation procedure is also developed. Extensive simulations and a real data analysis are conducted to validate the effectiveness of the proposed estimation approach.

ABSTRACT Distributional regression extends generalized additive models by linking all distributional parameters to covariates. Gradient boosting is among the most effective estimation techniques for such models, yet it can suffer from vanishing gradients, resulting in unstable updates and weak variable selection. We introduce stagewise boosting for distributional regression, using sign‐based, semiconstant step updates to stabilize learning. The method includes the best‐subset updating across parameters and a correlation filtering criterion for regularization and early stopping, with batchwise variants for large data. Simulations and a lightning count application with 9.1 million observations and 672 covariates demonstrate improved selection accuracy, predictive calibration and scalability. The approach provides a robust, computationally efficient alternative to gradient‐based boosting in distributional regression.

ABSTRACT In recent years, the rapid advancement of data collection and processing technologies has led to a growing influx of high‐dimensional data into various scientific fields. However, this surge in data is often accompanied by the frequent occurrence of outliers, particularly in domains such as genomic and image data. If these outliers are not appropriately addressed, they can result in biased or invalid models that may mislead subsequent statistical inference based on the data. Building upon the minimum distance and kernel density estimator, this paper thus proposes a new method named minimum distance kernel estimation (MDKE) to overcome the problems caused by the outliers in data. We construct the objective function of MDKE by employing the kernel technique. The advantage of MDKE over existing approaches is that it is robust to both outliers and high‐leverage points and does not rely on a prespecified parametric form for the error distribution. Furthermore, the sparse MDKE (SMDKE) is proposed for high‐dimensional data by inducing the regularizations such as LASSO, SCAD and MCP. The extensive simulation studies are conducted, demonstrating that MDKE exhibits superior robustness than the existing methods for data with outliers in both the response and covariates. Analyses of real‐world datasets involving plasma beta‐carotene levels and microarray gene expression further demonstrate the superior robustness and variable selection performance of the proposed SMDKE method compared to existing alternatives.

ABSTRACT Canonical correlation analysis (CCA) is a powerful technique for assessing the relationship between two sets of variables. However, classical CCA does not distinguish between treatment and outcome variables, and it fails to account for potential confounding effects that may bias the estimated results. This study proposes a novel method called canonical causal analysis (Causal‐CCA) that extends CCA to estimate the canonical causal effects between multivariate continuous treatments and outcomes while adjusting for confounding variables. Causal effects are estimated within a framework where treatments and outcomes are prespecified. The proposed approach uses Gram–Schmidt orthogonalization and entropy balancing weights for multivariate treatments (EBMT) to extract unconfounded canonical causal variates and compute the canonical causal effects. Extensive simulations across various scenarios demonstrate that Causal‐CCA consistently outperforms classical CCA, weighted CCA with multivariate generalized propensity score weighting (MVGPS) and CCA with EBMT in terms of bias and mean squared error. The proposed method is applied to a real‐world dataset to study the causal relationship between psychological factors (self‐concept and motivation) and academic achievement (math and science scores), showing a significant positive causal effect of the psychological variables on academic performance.

ABSTRACTImaging genetics–based mediation analysis provides a powerful approach to understanding gene–brain–cognition pathways. However, despite recent progress, several challenges involving group‐level and subject‐level heterogeneity remain largely unaddressed. In this article, we develop a new model and the associated methodology for imaging genetics–based subgroup mediation analysis. Our key idea is to equip a system of structural equation models with conditional Gaussian graphical models, and we allow both the mean and precision matrix to vary based on individual covariates, which in turn define a set of latent clusters. As a result, our model can simultaneously identify gene–brain–cognition pathways, uncover brain connectivity network structures, handle high‐dimensional multivariate mediators and incorporate both group‐level and subject‐level heterogeneity. We carry out simulations to demonstrate the efficacy of our proposed method and further illustrate the method with an image genetics study of Alzheimer's disease.

No abstract is available for this article.

ABSTRACTWe consider the general performance of the difference‐in‐means estimator in an equally‐allocated two‐arm randomized experiment under common experimental endpoints such as continuous (regression), incidence, proportion, count and uncensored survival. We consider two sources of randomness: the subject‐specific assignments and the contribution of unobserved subject‐specific measurements. We then examine mean squared error (MSE) performance under a new, more realistic simultaneous tail criterion. We prove that the pairwise matching design asymptotically performs best under the simultaneous tail criterion when compared with other blocking designs for all response types. We also prove that the optimal design must be less random than complete randomization and more random than any deterministic, optimized allocation. Theoretical results are supported by simulations.