🤖 AI Summary
High-dimensional educational data often exhibit sparsity, grouped predictor structures, and local correlations, which limit the performance of traditional regression methods. This work proposes an adaptive weighted group-fused LASSO estimator that simultaneously achieves adaptive variable selection, group-wise sparsity regularization, and coefficient fusion within a unified penalized regression framework. An efficient ADMM algorithm is developed for computation. The method uniquely integrates these three components and enjoys strong theoretical guarantees, including model selection consistency, the oracle property, and debiased asymptotic normality. Empirical results demonstrate its superior estimation accuracy and predictive performance over existing penalized approaches. Applied to Alabama state mathematics achievement data, the proposed method significantly enhances model interpretability and prediction accuracy while effectively identifying key school-level determinants.
📝 Abstract
High-dimensional educational datasets often exhibit sparsity, grouped predictors, and locally correlated covariates, limiting the effectiveness of conventional regression methods. We propose an Adaptive Weighted Group Fused LASSO estimator that jointly performs adaptive variable selection, group regularization, and coefficient fusion within a unified penalized regression framework. An efficient ADMM algorithm is developed, and asymptotic properties, including consistency, oracle property, and debiased asymptotic normality, are established. Simulation studies demonstrate superior estimation and prediction performance compared with existing penalized methods. An application to Alabama public school mathematics proficiency data illustrates improved model interpretability, predictive accuracy, and identification of the most influential institutional predictors.