Advertisement

Robust estimation: A condensed partial survey

  • Frank R. Hampel
Article

Keywords

Stochastic Process Probability Theory Mathematical Biology Robust Estimation Partial Survey 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, T.W.: An Introduction to Multivariate Statistical Analysis. New York: Wiley 1958Google Scholar
  2. Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H., Tukey, J.W.: Robust Estimates of Location: Survey and Advances. Princeton: Princeton University Press (1972)Google Scholar
  3. Anonymous: Dissertation sur la recherche du milieu le plus probable. Ann. Math. Pures et Appl., 12, 181–204 (1821)Google Scholar
  4. Anscombe, F.J.: Rejection of outliers. Technometrics, 2, 123–147 (1960)Google Scholar
  5. Anscombe, F.J.: Topics in the investigation of linear relations fitted by the method of least squares. J. Roy. Statist. Soc. Ser. B, 29, 1–52 (1967)Google Scholar
  6. Anscombe, F.J., Tukey, J.W.: The examination and analysis of residuals. Technometrics, 5, 141–160 (1963)Google Scholar
  7. åström, K.J.: Introduction to Stochastic Control Theory. New York and London: Academic Press 1970Google Scholar
  8. Bahadur, R. R., Savage, L.J.: The nonexistence of certain statistical procedures in nonparametric problems. Ann. Math. Statist., 27, 1115–1122 (1956)Google Scholar
  9. Bessel, F.W.: Fundamenta Astronomiae. Königsberg: Nicolovius (1818)Google Scholar
  10. Bickel, P.J.: On some analogues to linear combinations of order statistics in the linear model. Manuscript. (1971)Google Scholar
  11. Box, G. E. P.: Non-normality and tests on variances. Biometrika, 40, 318–335 (1953)Google Scholar
  12. Box, G. E. P., Andersen, S.L.: Permutation theory in the derivation of robust criteria and the study of departures from assumption. J. Roy. Statist. Soc. Ser. B, 17, 1–34 (1955)Google Scholar
  13. Box, G. E. P., Tiao, G.C.: A further look at robustness via Bayes' theorem. Biometrika, 49, 419–432 (1962)Google Scholar
  14. Chauvenet, W.: Manual of Spherical and Practical Astronomy. Philadelphia: Lippincott (1863)Google Scholar
  15. Cushny, A. R., Peebles, A. R.: The action of optical isomers. II. Hyoscines. Journal of Physiology, 32, 501–510 (1905)Google Scholar
  16. Daniel, C.: Locating outliers in factorial experiments. Technometrics, 2, 149–156 (1960)Google Scholar
  17. Daniel, C.: Statistical aids in the planning of experimental work. Course at the University of California, Berkeley (1968)Google Scholar
  18. Daniel, C., Wood, F.S.: Fitting Equations to Data. Computer Analysis of Multifactor Data for Scientists and Engineers. New York: Wiley-Interscience (1971)Google Scholar
  19. De Finetti, B.: The Bayesian approach to the rejection of outliers. Proc. 4th Berkeley Sympos. Math. Statist. Probab., 1, 199–210. Berkeley and Los Angeles: University of California Press (1961)Google Scholar
  20. De Finetti, B.: Foresight: its logical laws, its subjective sources. (French original 1937.) Translation in: H.E. Kyburg and H.E. Smokier (ed.): Studies in Subjective Probability. New York: Wiley 1964Google Scholar
  21. Eisenhart, C.: Mendeleev's expressed preference (1895) of the 33 1/3%-trimmed mean. Memorandum, Nat. Bureau of Standards, Washington D.C. 1971Google Scholar
  22. Feller, W.: An Introduction to Probability Theory and Its Applications. Vol. II. New York: Wiley 1966Google Scholar
  23. Ferguson, T.S.: On the rejection of outliers. Proc. 4th Berkeley Sympos. Math. Statist. Probab., 1, 253–287. Berkeley and Los Angeles: University of California Press (1961)Google Scholar
  24. Fisher, R.A.: A mathematical examination of the methods of determining the accuracy of an observation by the mean error and by the mean square error. Monthly Not. Roy. Astron. Soc., 80, 758–770 (1920)Google Scholar
  25. Fisher, R.A.: On the mathematical foundations of theoretical statistics. Philos. Trans. Roy. Soc. London Ser. A, 222, 309–368 (1922)Google Scholar
  26. Fisher, R.A.: Statistical Methods for Research Workers. Edinburgh: Oliver & Boyd ((1925) 1970)Google Scholar
  27. Fisher, R.A.: The moments of the distribution for normal samples of measures of departure from normality. Proc. Roy. Soc. London, Ser. A, 130, 16–28 (1930)Google Scholar
  28. Fisher, R.A.: Uncertain inference. Proc. Amer. Acad. Arts and Sciences, 71, 245–258 (1936)Google Scholar
  29. Fisher, R.A., Thornton, H. G., Mackenzie, W. A.: The accuracy of the plating method of estimating the density of bacterial populations. Ann. Appl. Biology, 9, 325–359 (1922)Google Scholar
  30. Freedman, H.W.: The “little variable factor”. A statistical discussion of the reading of seismograms. Bull. Seismol. Soc. of America, 56, 593–604 (1966)Google Scholar
  31. Gauss, C.F.: Göttingische gelehrte Anzeigen (1821). Reprinted in: Werke, 4, 98. Göttingen: Dieterich 1880Google Scholar
  32. Geary, R.C.: Testing for normality. Biometrika, 34, 209–242 (1947)Google Scholar
  33. Gebhardt, F.: On the effect of stragglers on the risk of some mean estimators in small samples. Ann. Math. Statist., 37, 441–450 (1966)Google Scholar
  34. Gnanadesikan, R., Kettenring, J.R.: Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics, 28, 81–124 (1972)Google Scholar
  35. Grubbs, F.E.: Procedures for detecting outlying observations in samples. Technometrics, 11, 1–21 (1969)Google Scholar
  36. Hampel, F.R.: Contributions to the theory of robust estimation. Unpublished dissertation, Berkeley: University of California (1968)Google Scholar
  37. Hampel, F.R.: A general qualitative definition of robustness. Ann. Math. Statist., 42, 1887–1896 (1971)Google Scholar
  38. Hampel, F.R.: The influence curve and its role in robust estimation. Manuscript (1972)Google Scholar
  39. Hodges, J.L.: Efficiency in normal samples and tolerance of extreme values for some estimates of location. Proc. Fifth Berkeley Sympos. Math. Statist. Probab., 1965/1966, 1, 163–186, Berkeley and Los Angeles: Univ. Cal. Press (1967)Google Scholar
  40. Hodges, J.L., Lehmann, E.L.: The use of previous experience in reaching statistical decisions. Ann. Math. Statist., 23, 396–407 (1952)Google Scholar
  41. Huber, P.J.: Robust estimation of a location parameter. Ann. Math. Statist., 35, 73–101 (1964)Google Scholar
  42. Huber, P.J.: A robust version of the probability ratio test. Ann. Math. Statist., 36, 1753–1758 (1965)Google Scholar
  43. Huber, P.J.: Robust confidence limits. Z. Wahrscheinlichkeitstheorie und verw. Gebiete, 10, 269–278 (1968a)Google Scholar
  44. Huber, P.J.: Robust estimation. Mathematical Centre Tracts, 27, 3–25 (Amsterdam) (1968b)Google Scholar
  45. Huber, P.J.: Théorie de l'inférence statistique robuste. Montréal: Presses de l'Université de Montréal (1969)Google Scholar
  46. Huber, P.J.: Robust regression. Unpublished manuscript (1970a)Google Scholar
  47. Huber, P.J.: Studentizing robust estimates. In: Nonparametric Techniques in Statistical Inference (ed. M.L. Puri), 453–463. Cambridge: Cambridge Univ. Press (1970b)Google Scholar
  48. Huber, P.J.: Robust statistics: a review. Ann. Math. Statist., 43, 1041–1067 (1972)Google Scholar
  49. Huber, P.J.: Robust regression. To appear in: Ann. Statist, 1, No. 5, 1973aGoogle Scholar
  50. Huber, P.J.: Robustness and designs. To appear in: Proceedings of the Internat. Sympos. on Statistical Design and Linear Models. Fort Collins: Colorado State Univ. 1973 bGoogle Scholar
  51. Huber, P.J., Strassen, V.: The Neyman-Pearson lemma for capacities. Ann. Statist., 1, 251–263 (1973)Google Scholar
  52. Huber-Carol, C.: Etude asymptotique de tests robustes. Dissertation, ETH Zürich (1970)Google Scholar
  53. Jeffreys, H.: An alternative to the rejection of outliers. Proc. Roy. Soc. London Ser. A, 137, 78–87 (1932)Google Scholar
  54. Jeffreys, H.: Theory of Probability. Oxford: Clarendon Press, 1939, 1948, 1961Google Scholar
  55. Johnson, N.L., Leone, F.C.: Statistics and Experimental Design: In Engineering and the Physical Sciences. Vol. I. New York: Wiley 1964Google Scholar
  56. Kempthorne, O.: Some aspects of experimental inference. J. Amer. Statist. Assoc., 61, 11–34 (1966)Google Scholar
  57. Kruskal, W., Ferguson, T.S., Tukey, J.W., Gumbel, E.J.: Discussion of the papers of Messrs. Anscombe and Daniel. Technometrics, 2, 157–166 (1960)Google Scholar
  58. Lehmann, E.L.: Testing Statistical Hypotheses. New York: Wiley 1959Google Scholar
  59. Mandelbrot, B., Wallis, J.R.: Noah, Joseph, and operational hydrology. Water Resources Research, 4, 909–918 (1968)Google Scholar
  60. Merrill, H.M., Schweppe, F. C.: Bad data suppression in power system static state estimation. IEEE Trans., PAS-90, 2718–2725 (1971)Google Scholar
  61. Newcomb, S.: A generalized theory of the combination of observations so as to obtain the best result. Amer. J. Math., 8, 343–366 (1886)Google Scholar
  62. Pearson, E.S.: The analysis of variance in cases of non-normal variation. Biometrika, 23, 114–133 (1931)Google Scholar
  63. Peirce, B.: Criterion for the rejection of doubtful observations. Astronom. J., 2, 161–163 (1852)Google Scholar
  64. Pfanzagl, J.: Allgemeine Methodenlehre der Statistik. Vol. II. Berlin: de Gruyter 1968 (Sammlung Göschen)Google Scholar
  65. Quenouille, M.H.: Rapid Statistical Calculations. London: Griffin (1959)Google Scholar
  66. Romanowski, M., Green, E.: Practical applications of the modified normal distribution. Bull. Géodésique, 76, 1–20 (1965)Google Scholar
  67. Sachs, L.: Statistische Auswertungsmethoden. (3rd. Ed.) Berlin-Heidelberg-New York: Springer 1972Google Scholar
  68. Stigler, S.M.: Simon Newcomb, Percy Daniell, and the history of robust estimation 1885–1920. Submitted to J. Amer. Statist. Assoc. (1973)Google Scholar
  69. Strassen, V.: Messfehler und Information. Z. Wahrscheinlichkeitstheorie und verw. Gebiete, 2, 273–305 (1964)Google Scholar
  70. “Student”: The probable error of a mean. Biometrika, 6, 1–25 (1908)Google Scholar
  71. “Student”: Errors of routine analysis. Biometrika, 19, 151–164 (1927)Google Scholar
  72. Thomas, J.B.: An Introduction to Statistical Communication Theory. New York: Wiley 1969Google Scholar
  73. Tukey, J.W.: A survey of sampling from contaminated distributions. In: Contrib. to Prob. and Statist. (ed. Olkin), 448–485. Stanford: Stanford University Press (1960)Google Scholar
  74. Tukey, J.W.: The future of data analysis. Ann. Math. Statist., 33, 1–67 (1962)Google Scholar
  75. Tukey, J.W.: Exploratory Data Analysis. 3 Vol. Limited Preliminary Edition. Reading-Menlo Park-London-Don Mills: Addison-Wesley (1970/71)Google Scholar
  76. Tukey, J.W., McLaughlin, D.H.: Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/Winsorization I. Sankhyā Ser. A, 25, 331–352 (1963)Google Scholar
  77. von Mises, R.: On the asymptotic distributions of differentiable statistical functions. Ann. Math. Statist., 18, 309–348 (1947)Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Frank R. Hampel
    • 1
  1. 1.Seminar für Angewandte Mathematik der UniversitÄtZürichSwitzerland

Personalised recommendations