A Rank Minrelation - Majrelation Coefficient
This work addresses variable selection and network inference challenges in statistics, but it appears incremental as it builds on existing concepts like Lin's concordance coefficient.
The authors tackled the problem of detecting relevant variables in statistical analysis by proposing a new asymmetric bivariate measure called the rank minrelation coefficient, which estimates p(Y > X) for continuous variables and shows improved properties for variable selection compared to correlation in key examples.
Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical coefficient that we call the rank minrelation coefficient. We define a minrelation of X to Y (or equivalently a majrelation of Y to X) as a measure that estimate p(Y > X) when X and Y are continuous random variables. The approach is similar to Lin's concordance coefficient that rather focuses on estimating p(X = Y). In other words, if a variable X exhibits a minrelation to Y then, as X increases, Y is likely to increases too. However, on the contrary to concordance or correlation, the minrelation is not symmetric. More explicitly, if X decreases, little can be said on Y values (except that the uncertainty on Y actually increases). In this paper, we formally define this new kind of bivariate dependencies and propose a new statistical coefficient in order to detect those dependencies. We show through several key examples that this new coefficient has many interesting properties in order to select relevant variables, in particular when compared to correlation.