Abstract
A robust statistical procedure can be thought of as one which performs well over a range of situations and is able to stand up to a certain amount of abuse without breaking down. The development of the principal ideas of robustness is traced from about 1800 to the present, illustrating that scientists and statisticians have been concerned with the sensitivity of statistical procedures over this whole time and that some of the proposed solutions are closely related to robust estimates in use today. A brief overview of current research in robustness is given.
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Bibliography
Anonymous (1821). “Dissertation sur la recherche du milieu le plus probable,” Ann. Math. Pures et Appl., 12, 181–204.
Box, G. E. P. (1980). “Sampling and Bayes inference in scientific modelling and robustness,” J. Roy. Statist. Soc. Ser. A, 143, 383–430.
Chauvenet, W. (1863). A Manual of Spherical and Practical Astronomy, Vol. 2, Philadelphia: Lippincott.
Cushny, A. R. and Peebles, A. R. (1905). “The action of optical isomers. II. Hyoscines.” J. Physiol., 32, 501–510.
Daniell, P. J. (1920). “Observations weighted according to order.” Amer. J. Math., 42, 222–236.
Freeman, D., Pisani, R., and Purves, R. (1978). Statistics. New York: Norton.
Graf, H. P. (1983). Long Range Correlations and Estimation of the Self Similarity Parameter. Published Ph.D. Thesis. Zurich: E.T.H.
Hampel, F. R. (1973). “Robust estimation: a Condensed partial survey.” Z. Wahrsch. Verw. Gebiete, 27, 87–104.
Hampel, F. R., Ronchetti, E., Rousseeuw, P. J., an Stahel, W. (1985). Robust Statistics: The Approach Based on the Influence Function. New York: Wiley (to be published).
Hoaglin, D. C., Mosteller, F., and Tukey, J. W. (1983). Understanding Robust and Exploratory Data Analysis. New York: Wiley.
Huber, P. J. (1972). “Robust statistics: A review.” Ann. Math. Statist., 43, 1041–1067.
Huber, P. J. (1981). Robust Statistics. New York: Wiley.
Jeffreys, H. (1932). “An alternative to the rejection of outliers.” Proc. Roy. Soc. Ser. A, 137, 78–87.
Kleiner, B., Martin, R. D., and Thompson, D. J. (1979). “Robust estimation of power spectra.” J. Roy. Statist. Soc. Ser. B, 41, 313–351.
Laplace, P. S. de (1979). Traité de Mécanique Céleste, Paris: Gauthier-Villars.
Newcomb, S. (1886). “A generalized theory of the combination of observations so as to obtain the best result.” Amer. I. Math., 8, 343–366.
Newcomb, S. (1912). “Researches on the motion of the moon, II.” In Astronomical Papers, 9. U.S. Nautical Almanac Office, 1–249.
Pearson, E. S. (1931). “The analysis of variance in cases of non-normal variation.” Biometrika, 23, 114–133.
Peirce, B. (1852). “Criterion for the rejection of doubtful observations.” Astronom. J., 2, 161–163.
Saaty, T. L. and Bram, J. (1964). Nonlinear Mathematics. New York: McGraw-Hill.
Smith, R. H. (1888). “True average of observations?” Nature, 37, 464. Reproduced in Biometrika (1980), 67, 219–220.
Stigler, S. M. (1973). “Simon Newcomb, Percy Daniell, and the history of robust estimation 1885–1920.” J. Amer. Statis. Assoc., 68, 872–879.
Stigler, S. M. (1980). “Studies in the history of Probability and Statistics XXXVIII, R. H. Smith; a Victorian interested in robustness.” Biometrika, 67, 217–221.
“Student” (1927). “Errors of routine analysis.” Biometrika, 19, 151–164
Tukey, J. W. (1977). Exploratory Data Analysis. Reading, MA: Addison-Wesley.
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Field, C. (1985). Concepts of Robustness. In: Atkinson, A.C., Fienberg, S.E. (eds) A Celebration of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8560-8_15
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DOI: https://doi.org/10.1007/978-1-4613-8560-8_15
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