Deriving Nonlinear Correlation Coefficients from Partial Moments

Abstract

We introduce a nonlinear correlation coefficient metric derived from partial moments that can be substituted for the Pearson correlation coefficient in linear instances as well. The flexibility offered by partial moments enables ordered partitions of the data whereby linear segments are aggregated for an overall correlation coefficient. Our coefficient works without the need to perform a linear transformation on the underlying data, and can also provide a general measure of nonlinearity between two variables. We also extend the analysis to a multiple nonlinear regression without the adverse effects of multicollinearity.