Measuring non-linear dependence for two random variables distributed along a curve
We propose new dependence measures for two real random variables not necessarily linearly related. Covariance and linear correlation are expressed in terms of principal components and are generalized for variables distributed along a curve. Properties of these measures are discussed. The new measures are estimated using principal curves and are computed for simulated and real data sets. Finally, we present several statistical applications for the new dependence measures.
dependence measures principal curves independence tests linearity tests renyi's axioms similarity measures for pairs of variables