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A Rank Minrelation - Majrelation Coefficient
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
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