  By considering a least squares approximation of a given square integrable
function f:[0,1]^n --> R by a shifted L-statistic function (a shifted linear
combination of order statistics), we define an index which measures the global
influence of the k-th largest variable on f. We show that this influence index
has appealing properties and we interpret it as an average value of the
difference quotient of f in the direction of the k-th largest variable or,
under certain natural conditions on f, as an average value of the derivative of
f in the direction of the k-th largest variable. We also discuss a few
applications of this index in statistics and aggregation theory.
