  We present multiply subtractive Kramers-Kronig (MSKK) relations for the
moments of arbitrary order harmonic generation susceptibility. Using
experimental data on third-harmonic wave from polysilane, we show that singly
subtractive Kramers-Kronig (SSKK) relations provide better accuracy of data
inversion than the conventional Kramers-Kronig (K-K) relations. The fundamental
reason is that SSKK and MSKK relations have strictly faster asymptotic
decreasing integrands than the conventional K-K relations. Therefore SSKK and
MSKK relations can provide a reliable optical data inversion procedure based on
the use of measured data only.
