Abstract

In this talk, we address estimation and prediction problems in regression models where the regression coefficients may be constrained to lie in a candidate subspace, considering both low- and high-dimensional settings. We propose penalized, pretest, and shrinkage estimation methods and establish their large-sample properties through analyses of asymptotic distributional quadratic bias and risk.

Monte Carlo simulations are conducted to support the theoretical findings and to assess the finite-sample performance of the proposed estimators. In addition, real data applications—including comparisons with standard penalized methods, as well as machine learning–based approaches—demonstrate the practical effectiveness of our methodology.

Our proposed strategies consistently outperform competing methods over meaningful regions of the parameter space induced by the commonly adopted sparsity assumption. Moreover, they continue to perform well even when this assumption is substantially violated, providing strong evidence of their robustness.