A fast robust method for fitting gamma distributions
The art of fitting gamma distributions robustly is described. In particular we compare methods of fitting via minimizing a Cramér Von Mises distance, an L 2 minimum distance estimator, and fitting a B-optimal M-estimator. After a brief prelude on robust estimation explaining the merits in terms of weak continuity and Fréchet differentiability of all the aforesaid estimators from an asymptotic point of view, a comparison is drawn with classical estimation and fitting. In summary, we give a practical example where minimizing a Cramér Von Mises distance is both efficacious in terms of efficiency and robustness as well as being easily implemented. Here gamma distributions arise naturally for “in control” representation indicators from measurements of spectra when using fourier transform infrared (FTIR) spectroscopy. However, estimating the in-control parameters for these distributions is often difficult, due to the occasional occurrence of outliers.
KeywordsGamma distributions Fréchet differentiability Weak continuity Robust estimation Minimum distance estimation
Mathematics Subject Classification (2000)62F35 62-07
Unable to display preview. Download preview PDF.
- Andrews DF, Bickel PJ, Hampel FR, Huber PJ, Rogers WH, Tukey JW (1972) Robust estimates of location: advances. Princeton University Press,Google Scholar
- Clarke BR (2000b) A review of differentiability in relation to robustness with an application to seismic data analysis. Proc Indian Natl Sci Acad A 66: 467–482Google Scholar
- Eyer S, Riley G (1999) Measurement quality assurance in a production system for bauxite analysis by FTIR. N Am Chapter Int Chemom Soc. Newsl No. 19Google Scholar
- Marazzi A, Ruffieux C (1996) Implementing M-estimators of the gamma distribution. In: Rieder H (ed) Robust statistics, data analysis, and computer intensive methods. In: Honor of Peter Huber’s 60th birthday. Lecture notes in statistics. Springer, Heidelberg, pp 277–297Google Scholar