A Rank Minrelation - Majrelation Coefficient

摘要

Improving the detection of relevant variables using a new bivariate measurecould importantly impact variable selection and large network inferencemethods. In this paper, we propose a new statistical coefficient that we callthe rank minrelation coefficient. We define a minrelation of X to Y (orequivalently a majrelation of Y to X) as a measure that estimate p(Y > X) whenX and Y are continuous random variables. The approach is similar to Lin'sconcordance coefficient that rather focuses on estimating p(X = Y). In otherwords, if a variable X exhibits a minrelation to Y then, as X increases, Y islikely to increases too. However, on the contrary to concordance orcorrelation, the minrelation is not symmetric. More explicitly, if X decreases,little can be said on Y values (except that the uncertainty on Y actuallyincreases). In this paper, we formally define this new kind of bivariatedependencies and propose a new statistical coefficient in order to detect thosedependencies. We show through several key examples that this new coefficienthas many interesting properties in order to select relevant variables, inparticular when compared to correlation.