Margon, M., and Bowyer, S. 1976, Astrophysical Journal, vol. 208, pp. 177–190. Brownlee, . 1965, Statistical Theory and Methodology, 2nd ed. (New York: Wiley). Martin, . 1971, Statistics for Physicists (New York: Academic Press) | Robust Estimation 699 Cjk X VjiVki i 1 CITED REFERENCES AND FURTHER READING Efron B. 1982 The Jackknife the Bootstrap and Other Resampling Plans Philadelphia . . 1 Efron B. and Tibshirani R. 1986 Statistical Science vol. 1 pp. 54-77. 2 Avni Y. 1976 Astrophysical Journal vol. 210 pp. 642-646. 3 Lampton M. Margon M. and Bowyer S. 1976 Astrophysical Journal vol. 208 pp. 177-190. Brownlee . 1965 Statistical Theory and Methodology 2nd ed. New York Wiley . Martin . 1971 Statistics for Physicists New York Academic Press . Robust Estimation The concept of robustness has been mentioned in passing several times already. In we noted that the median was a more robust estimator of central value than the mean in it was mentioned that rank correlation is more robust than linear correlation. The concept of outlier points as exceptions to a Gaussian model for experimental error was discussed in . The term robust was coined in statistics by . Box in 1953. Various definitions of greater or lesser mathematical rigor are possible for the term but in general referring to a statistical estimator it means insensitive to small departures from the idealized assumptions for which the estimator is optimized. 1 2 The word small can have two different interpretations both important either fractionally small departures for all data points or else fractionally large departures for a small number of data points. It is the latter interpretation leading to the notion of outlier points that is generally the most stressful for statistical procedures. Statisticians have developed various sorts of robust statistical estimators. Many if not most can be grouped in one of three categories. M-estimates follow from maximum-likelihood arguments very much as equations and followed from equation . M-estimates are usually the most relevant class for model-fitting that is estimation of parameters. We therefore consider these estimates in some
