Sliced Inverse Regression for the inference of stellar fundamental parameters

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.