2023/07/06 by Daeyoung Ham, Ham, Daeyoung, Adam J. Rothman +1
Computer Science · #FOS: Computer and information sciences #Face and Expression Recognition #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.2307.03317
openalex publication_date 2023/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a penalized least-squares method to fit the linear regression model with fitted values that are invariant to invertible linear transformations of the design matrix. This invariance is important, for example, when practitioners have categorical predictors and interactions. Our method has the same computational cost as ridge-penalized least squares, which lacks this invariance. We derive the expected squared distance between the vector of population fitted values and its shrinkage estimator as well as the tuning parameter value that minimizes this expectation. In addition to using cross validation, we construct two estimators of this optimal tuning parameter value and study their asymptotic properties. Our numerical experiments and data examples show that our method performs similarly to ridge-penalized least-squares.