Precessional parameters obtained from biased data of Hipparcos-FK5 proper motions

The Hipparcos catalogue provides a reference frame in optical wavelength for the new ICRS. The differences in the system of proper motions of Hipparcos and the previous materialization of the reference frame, the FK5, are expected to be caused only by the combined effects of the motion of the equinox of the FK5 as well as the Luni-solar and planetary precession, but several authors have signaled the existence of an inconsistency for the proper motion differences of the FK5-Hipparcos with the ∆p values corresponding to the Luni-solar precession as determined from VLBI and LLR It is a fact that the widely employed parametric models do not remove the bias in the random variables. The introduction of a non parametric method, combined with the inner product in L over S shows the necessity of removing the bias. The precessional formulas should be rearranged to be used in this case. When applying this model, the obtained values for the precession corrections are very consistent with the ones currently adopted by the IAU.