  We aim at finding the value of an explanatory variable, through its
expression in a large data-vector, without knowing the link function between
the explanatory variable and the data-space. Sliced Inverse Regression (SIR)
method allows for the projection of a data-vector onto a subspace consistent
with the explanatory variable variation. We suggest a method based on the SIR
subspace, that gives the most efficient estimation of an unknown explanatory
variable.
