Determinacy in the linear model: Gauss to Bose and Koopmans

International Statistical Review

Volumn 67, Issue 2, 1999, Pages 211-219

  Aldrich, John ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Collinearity; Estimability; Fidelity; Gauss; Identifiability; Least squares; Rank

Indexed keywords

EID: 0033169290     PISSN: 03067734     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1751-5823.1999.tb00427.x     Document Type: Article

References (41)

1. Aitken, A.C. (1935). On Least Squares and Linear Combinations of Observations. Proceedings of the Royal Society of Edinburgh, 55, 42-48.
2. Aitken, A.C. (1945). Studies in Practical Mathematics. IV. On Linear Approximation by Least Squares. Proceedings of the Royal Society of Edinburgh, 62, 138-146.
3. Aldrich, J. (1994). Haavelmo's Identification Theory. Econometric Theory, 10, 198-219.
4. Aldrich, J. (1998). Doing Least Squares: Perspectives from Gauss and Yule. International Statistical Review, 66, 61-81.
5. Bose, R.C. (1944). The Fundamental Theorem of Linear Estimation. Proceedings of the 31st Indian Scientific Congress, (abstract) 2-3.
6. Chauvenet, W. (1891). A Manual of Spherical and Practical Astronomy, volume 2, fifth edition, reprinted by Dover 1960.
7. Chipman, J.S. (1964). On Least Squares with Insufficient Observations. Journal of the American Statistical Association, 59, 1078-1111.
8. Dale, A.I. (1991). A History of Inverse Probability from Thomas Bayes to Karl Pearson. New York: Springer-Verlag.
9. David, F.N. & Neyman, J. (1938). Extension of the Markoff Theorem on Least Squares. Statistical Research Memoirs, University College London, 2, 105-116.
10. Durbin, J. (1953). A Note on Regression when there is Extraneous Information about One of the Coefficients. Journal of the American Statistical Association, 48, 799-808.
11. Farebrother, R.W. (1996). Some Early Statistical Contributions to the Theory and Practice of Linear Algebra. Linear Algebra and its Applications, 237, 205-224.
12. Farebrother, R.W. (1997). A.C. Aitken and the Consolidation of Matrix Theory. Linear Algebra and its Applications, 264, 3-12.
13. Fisher, R.A. (1922). The Goodness of Fit of Regression Formulae, and the Distribution of Regression Coefficients. Journal of the Royal Statistical Society, 85, 597-612.
14. Fisher, R.A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver & Boyd.
15. Gauss, C.F. (1809). Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium. Hamburg: Perthes & Besser. English translation by C.H. Davis, reprinted 1963 Dover, New York.
16. Gauss, C.F. (1823/8). Theoria Combinationis Observationum Erroribus Minimus Obnoxiae, in two parts and a supplement. Commentatines Societatis Regiae Scientarum Gottingensis Recentiores, 5, 33-62 & 63-90, 6, 57-93. Reprinted with facing English translation and notes by G.W. Stewart, (1995). Philadelphia: SIAM.
17. Gauss, C.F. (1855). Methode des Moindres Carrés, a translation into French of Gauss's memoirs on least squares by J.Bertrand. Paris: Mallet-Bachelier.
18. Goldstine, H. (1977). A History of Numerical Analysis from the 16th through the 19th Century. New York: Springer-Verlag.
19. Hald, A. (1998). A History of Mathematical Statistics from 1750 to 1930. New York: Wiley.
20. Koopmans, T.C. & Reiersøl, O. (1950). The Identification of Structural Characteristics. Annals of Mathematical Statistics, 21, 165-181.
21. Learner, E.E. (1978). Specification Searches. New York: Wiley.
22. Lidstone, G.J. (1933). Notes on Orthogonal Polynomials and their Application to Least-Square Methods etc. Journal of the Institute of Actuaries, 64, 128-164.
23. MacDuffee, C.C. (1933). The Theory of Matrices. Berlin: Springer.
24. Markov, A.A. (1912). Wahrscheinlichkeitsrechnung, second edition. Leipzig: Teubner.
25. Merriman, M. (1877). A List of Writings Relating to the Method of Least Squares, with Historical and Critical Notes. Transactions of the Connecticut Academy of Arts and Sciences, 4, reprinted in volume I of Stigler (1980).
26. Merriman, M. (1877a). On the History of the Method of Least Squares. The Analyst, 4, reprinted in volume I of Stigler (1980).
27. Merriman, M. (1884). A Textbook on the Method of Least Squares. New York: Wiley.
28. Neyman, J. (1934). On the Two Different Aspects of the Representative Method. Journal of the Royal Statistical Society, 97, 558-606.
29. Plackett, R.L. (1949). A Historical Note on the Method of Least Squares. Biometrika, 36, 458-460.
30. Plackett, R.L. (1972). The Discovery of the Method of Least Squares. Biometrika, 59, 239-251.
31. Rao, C.R. (1945). Generalisation of Markoff's Theorem and Tests of Linear Hypotheses. Sankhya, 7, 9-16.
32. Rao, C.R. (1973). Linear Statistical Inference and its Applications, 2nd edition. New York: Wiley.
33. Seal, H.L. (1967). The Historical Development of the Gauss Linear Model. Biometrika, 54, 1-24.
34. Sheppard, W.F. (1912). Reduction of Errors by Means of Negligible Differences. Proceedings of the Fifth International Congress of Mathematicians (Cambridge), 2, 348-384.
35. Sprott, D.A. (1978). Gauss's Contributions to Statistics. Historia Mathematica, 5, 183-203.
36. Stewart, G.W. (1995). Gauss, Statistics, and Gaussian Elimination. Journal of Computational and Graphical Statistics, 4, 1-11.
37. Stigler, S.M. (1980). American Contributions to Mathematical Statistics in the Nineteenth Century, in two volumes. New York: Arno.
38. Stigler, S.M. (1986). The History of Statistics. Cambridge: Harvard University Press.
39. Stone, R. (1954). The Measurement of Consumers' Expenditure and Behaviour in the United Kingdom 1920-1938, volume 1. Cambridge: Cambridge University Press.
40. Waterhouse, W.C. (1990). Gauss's First Argument for Least Squares. Archive for the History of the Exact Sciences, 41, 41-52.
41. Whittaker, E. & Robinson, G. (1924). The Calculus of Observations. London: Blackie.