Robust Estimation in the Analysis of Complex Molecular Spectra

In atomic and molecular spectroscopy, measured transition energies represent differences between the energy levels of the emitting or absorbing system. In complex spectra of such transitions, the assignment of the pair of states corresponding to an observed transition energy is a difficult process....

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Bibliographic Details
Published inJournal of the American Statistical Association Vol. 89; no. 427; pp. 788 - 795
Main Authors Stahel, Werner A., Ruckstuhl, Andreas F., Senn, Peter, Dressler, Kurt
Format Journal Article
LanguageEnglish
Published Alexandria, VA Taylor & Francis Group 01.09.1994
American Statistical Association
Subjects
Analysis of variance
Applications
Applications and Case Studies
Biology, psychology, social sciences
Datasets
Energy
Energy levels
Energy value
Estimators
Exact sciences and technology
Insurance, economics, finance
LI estimation
Logistics
Mathematics
Medical sciences
Molecular spectra
Molecular spectroscopy
Molecules
Physical chemistry
Probability and statistics
Quantum numbers
Reliability, life testing, quality control
Sciences and techniques of general use
Statistics
Spectrometry
Fitting
Transition energy
Estimator robustness
Iterative method
Unbalanced design
Two way analysis of variance
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Summary:In atomic and molecular spectroscopy, measured transition energies represent differences between the energy levels of the emitting or absorbing 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 proven extremely helpful for finding gross errors and for obtaining reliable estimates of energy levels in the analysis of molecular tritium (T 2 ) spectra. The robust results can be used successfully to obtain new assignments of transition energies to energy levels. In statistical terms, a highly unbalanced two-way analysis of variance model results. Some specific robustness problems that call for further research are mentioned. An iterative algorithm that is fast and avoids storage problems, 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.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1994.10476812