We propose to estimate the CS using the difference of the means between the points that belong to the two sets A1, A2. We
denote this as:
md = E(XI( ˜ Y = 1)) − E(XI( ˜ Y = −1)). (3)
It is pretty straightforward to prove the following result. The assumption E(X|βTX) = PT
β(6)X is a very common
assumption in the SDR literature and it holds if the predictors are elliptically distributed