Penalized angular regression for personalized predictions

The method therefore penalizes the normalized regression coefficients, or the angles of the regression coefficients in a hyperspherical parametrization, introducing a new angle-based class of penalties. PAN hence combines two novel concepts: penalizing the normalized coefficients and personalization. For an orthogonal design matrix, we show that the PAN estimator is the solution to a low-dimensional eigenvector equation. Based on the hyperspherical parametrization, we construct an efficient algorithm to calculate the PAN estimator. We propose a parametric bootstrap procedure for selecting the tuning parameter, and simulations show that PAN regression can outperform ordinary least squares, ridge regression and other penalized regression methods in terms of prediction error. Finally, we demonstrate the method in a medical application.