On the history of maximum likelihood in relation to inverse probability and least squares

Statistical Science

Volumn 14, Issue 2, 1999, Pages 214-222

  Hald, Anders ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Chauvenet; Confidence limits; Credible limits; Edgeworth; Encke; Fisher; Gauss; Gosset; Hagen; Invariance; Inverse probability; Laplace; Least squares; Likelihood limits; Linear normal model; Maximum likelihood; Merriman; Posterior mode; Reparameterization; T distribution; Two stage maximum likelihood method; Unbiasedness

Indexed keywords

EID: 0043226670     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1009212248     Document Type: Article

References (30)

1. Aldrich, J. (1997). R. A. Fisher and the making of maximum likelihood 1912-1922. Statist. Sci. 12 162-176.
2. Chauvenet, W. (1863). On the method of least squares. In A Manual of Spherical and Practical Astronomy 2 469-566. Lippincott, Philadelphia. (An appendix.)
3. Edgeworth, F. Y. (1883). The method of least squares. Philos. Mag. (5) 16 360-375.
4. Edgeworth, F. Y. (1908). On the probable error of frequency constants. J. Roy. Statist. Soc. 71 381-397, 499-512, 651-678.
5. Edgeworth, F. Y. (1909). Addendum on “Probable errors of frequency constants.” J. Roy. Statist. Soc. 72 81-90.
6. Edwards, A. W. F. (1974). The history of likelihood. Internat. Statist. Rev. 42 9-15.
7. Edwards, A. W. F. (1997). What did Fisher mean by “inverse probability” in 1912-1922? Statist. Sci. 12 177-184.
8. Encke, J. F. (1832-1834). Uber die Methode der kleinsten Quadrate. In Berliner Astronomisches Jahrbuch für 1834 249-312;
9. Encke, J. F. (1832-1834). Uber die Methode der kleinsten Quadrate. In für 1835 253-320;
10. Encke, J. F. (1832-1834). Uber die Methode der kleinsten Quadrate. In für 1836 253-308.
11. Fisher, R. A. (1912). On an absolute criterion for fitting frequency curves. Messenger of Mathematics 41 155-160. [Reprinted in Statist. Sci. 12 (1997) 39-41.]
12. Fisher, R. A. (1915). Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika 10 507-521.
13. Fisher, R. A. (1921). On the “probable error” of a coefficient of correlation deduced from a small sample. Metron 1 3-32.
14. Fisher, R. A. (1922a). On the mathematical foundations of theoretical statistics. Philos. Trans. Roy. Soc. London Ser. A 222 309-368.
15. Fisher, R. A. (1922b). The goodness of fit of regression formulæ, and the distribution of regression coefficients. J. Roy. Statist. Soc. 85 597-612.
16. Gauss, C. F. (1809). Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium. Perthes et Besser, Hamburg.
17. Gauss, C. F. (1816). Bestimmung der Genauigkeit der Beobachtungen. Z. Astronom. Verwandte Wiss. 1 185-196.
18. Gauss, C. F. (1823). Theoria combinationis observationum er-roribus minimis obnoxiae. Comm. Soc. Reg. Gottingensis Rec. 5 33-62, 63-90.
19. Hagen, G. (1837). Grundzuge der Wahrscheinlichkeits Rechnung. Dummler, Berlin.
20. Hald, A. (1998). A History of Mathematical Statistics from 1750 to 1930. Wiley, New York.
21. Helmert, F. R. (1876). Die Genauigkeit der Formel von Peters zur Berechnung des wahrscheinlichen Beobachtungsfehler direchter Beobachtungen gleicher Genauigkeit. Astronom. Nachr. 88 113-132.
22. Laplace, P. S. de (1812). Théorie Analytique des Probabilités. Courcier, Paris.
23. Merriman, M. (1877). A list of writings relating to the method of least squares, with historical and critical notes. Trans. Conn. Acad. Arts Sci. 4 151-232.
24. Merriman, M. (1884). A Text-Book on the Method of Least Squares. Wiley, New York. [References are to the 8th ed. (1915).]
25. Neyman, J. and Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica 16 1-32.
26. Pearson, E. S. (1968). Some early correspondence between W. S. Gosset, R. A. Fisher and Karl Pearson, with notes and comments. Biometrika 55 445-457.
27. Pratt, J. W. (1976). F. Y. Edgeworth and R. A. Fisher on the efficiency of maximum likelihood estimation. Ann. Statist. 4 501-514.
28. Savage, L. J. (1976). On rereading R. A. Fisher. Ann. Statist. 4 441-483.
29. “Student” (1908). The probable error of a mean. Biometrika 6 1-25.
30. Todhunter, I. (1865). A History of the Mathematical Theory of Probability from the Time of Pascal to That of Laplace. Macmillan, London.