Journal of Data Science

In the linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components regression. WOCR makes use of the monotonicity inherent in orthogonal components to parameterize the weight function. The formulation allows for efficient determination of tuning parameters and hence is computationally advantageous. Moreover, WOCR offers insights for deriving new better variants. Specifically, we advocate assigning weights to components based on their correlations with the response, which may lead to enhanced predictive performance. Both simulated studies and real data examples are provided to assess and illustrate the advantages of the proposed methods.