r-PAmeasures

We propose a pair of summary measures for the predictive power of a prediction function based on a regression model. The regression model can be linear or nonlinear, parametric, semi-parametric, or nonparametric, and correctly specified or mis-specified. The first measure, R-squared, is an extension of the classical R-squared statistic for a linear model, quantifying the prediction function's ability to capture the variability of the response. The second measure, L-squared, quantifies the prediction function's bias for predicting the mean regression function. When used together, they give a complete summary of the predictive power of a prediction function. Please refer to Gang Li and Xiaoyan Wang (2016) <arXiv:1611.03063> for more details.