ROBUST ESTIMATION IN THE ANALYSIS OF COMPLEX MOLECULAR-SPECTRA

In atomic and molecular spectroscopy, measured transition energies rep resent differences between the energy levels of the emitting or absorb ing system. In complex spectra of such transitions, the assignment of the pair of states corresponding to an observed transition energy is a difficult process. These assignments evolve in stages. At each stage, some assignments will be erroneous. Robust fitting methods have prove n extremely helpful for finding gross errors and for obtaining reliabl e estimates of energy levels in the analysis of molecular tritium (T-2 ) spectra. The robust results can be used successfully to obtain new a ssignments of transition energies to energy levels. In statistical ter ms, a highly unbalanced two-way analysis of variance model results. So me specific robustness problems that call for further research are men tioned. An iterative algorithm that is fast and avoids storage problem s, even for large data sets, is described. This algorithm can be used for both least squares and robust fitting of incomplete two-way tables and similar designs.