Un indice général d association entre deux variables continues; A general non-linear index of association for two continuous variables

Measuring and assessing the degree of association between two continuous variables, say Xand Y, has heretofore been restricted by the mandatory specification of a parametric model, be it linear (simple or polynomial), cyclic, autoregressive, or other. We propose as a new quantifying principle the idea that, if a variable Yis in some way linked to a variable X, values of Yimmediately neighbouring on Xshould differ less than non-neighbouring ones, so that the permutative variance (i.e. variance of successive differences) of the Yconcomitants of Xshould be low. Two indices, one asymmetrical (Yon X), the other symmetrical (Ycum X), are explored and exemplified, and their appropriate critical values,power characteristics and relative merits are established.