Reweighted penalized regression for convenience samples

Abstract Modern epidemiological studies are often characterized by extensive data collection, which facilitates building high‐dimensional predictive models. With large samples often conveniently sampled, weighted penalized regression models are commonly applied to provide improved prediction. In this article, we empirically show that weighted ridge regression models may yield suboptimal results because of the lack of flexibility in the penalty structure. We propose a generalized weighted ridge regression (GWRR) estimation procedure that allows for the adjustment of sampling weights in the penalty structure. We derive the asymptotic properties of the proposed GWRR estimator and provide a computationally efficient closed‐form solution. We demonstrate the performance of the proposed GWRR estimator and justify the asymptotic variance via simulation studies. Finally, we illustrate the utility of our proposed estimator through an application to the prediction of mini‐mental state examination (MMSE) scores.