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Abstract

This paper is concerned with one of the enduringly central problems of statistics and, via applications, also of econometrics, biometrics, psychometrics, and indeed of any field of research concerned with identification from noisy data.

Keywords

Real Data Linear Relation Noise Environment Realization Theory Elliptical Orbit 
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.

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References

  1. [1]
    Anderson, T.W. and Rubin, H. (1956), “Statistical inference in factor analysis”, Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability, 5, pp. 111–150.Google Scholar
  2. [2]
    Box, J.F. (1978), “R.A. Fisher: The Life of a Scientist”, Wiley, 512 pages.Google Scholar
  3. [3]
    Cheney, E.W. (1963), “Introduction to Approximation Theory”, McGraw-Hill, 259 pages.Google Scholar
  4. [4]
    Davis, P.J. (1963), “Interpolation and Approximation”, Blaisdell, 393 pages.Google Scholar
  5. [5]
    Fisher, R.A. (1918), “On the correlation between relatives on the assumption of a Mendelian inheritance”, Transactions of the Royal Society of Edinburgh, 52, pp. 399–433.Google Scholar
  6. [6]
    Freedman, D., Pisani, R. and Purves, R. (1978), “Statistics”, Norton, 589 pages.Google Scholar
  7. [7]
    Frisch, R. (1934), “Statistical confluence analysis by means of complete regression systems”, Publication no. 5, University of Oslo Economic Institute, 192 pages.Google Scholar
  8. [8]
    Galton, F. (1886), “Family likeness in stature”, Proceedings of the Royal Society of London, 40, pp. 42–63.CrossRefGoogle Scholar
  9. [9]
    Gini, C. (1921), “Sull’interpolazione de una retta quando i valori delia variabile indipendente sono affetti da errori accidentali”, Metron, 1, pp. 63–82.Google Scholar
  10. [10]
    Gould, S.J. (1981), “The Mismeasure of Man”, Norton, 352 pages.Google Scholar
  11. [11]
    Haavelmo, T. (1943), “The statistical implications of a system of simultaneous equations”, Econometrica, 11, pp. 1–12.CrossRefGoogle Scholar
  12. [12]
    Harter, H.L. (1974–1976), “The method of least squares and some alternatives. Parts I-VI”, International Statistical Review, volumes 42–44.Google Scholar
  13. [13]
    Hotelling, H. (1933), “Analysis of complex statistical variables into principal components”, J. of Educational Psychology, 24, pp. 417–441, 498–520.CrossRefGoogle Scholar
  14. [14]
    Kaiman, R.E. (1980), “Identiflability and problems of model selection in econometrics”, vol. 2 of Proceedings of the 4th World Congress of the Econometric Society, (August-September 1980, Aix-en-Provence), Cambridge University Press.Google Scholar
  15. [15]
    Kaiman, R.E. (1981), “System-theoretic critique of dynamic economic models”, International J. of Policy Analysis and Information Systems, 4, pp. 3–22.Google Scholar
  16. [16]
    Kaiman, R.E. (1982a), “System identification from noisy data”, Proc. International Symposium on Dynamical Systems (Gainesville, FL February 1981), edited by A. Bednarek, Academic Press.Google Scholar
  17. [17]
    Kaiman, R.E. (1982b), “Identifiability and modeling in econometrics”, Developments in Statistics, edited by P.R. Krishanaiah, Academic Press, vol. 4.Google Scholar
  18. [18]
    Kaiman, R.E. (1983), “Identification of linear relations from noisy data”, to appear.Google Scholar
  19. [19]
    Kaiman, R.E., Falb, P.L. and Arbib, M.A. (1969), “Topics in Mathematical System Theory”, McGraw Hill, 358 pages.Google Scholar
  20. [20]
    Kendall, M.G. and Stewart, A. (1970), “The Advanced Theory of Statistics”, vol. 2, Griffin, 521 pages.Google Scholar
  21. [21]
    Koopmans, T.C. (1937), “Linear Regression Analysis of Economic Time Series”, Netherlands Economic Institute, 150 pages.Google Scholar
  22. [22]
    Koten, J. (1981), “They say no two economists ever agree, so Chrysler tries averaging their opinions”, The Wall Street Journal, November 3, 1981, p. 37.Google Scholar
  23. [23]
    Lawley, D.N. and Maxwell, A.E. (1971), “Factor Analysis as a Statistical Method”, second edition, Butterworths, 153 pages.Google Scholar
  24. [24]
    Learner, E.E. (1978), “Specification Searches”, Wiley, 370 pages.Google Scholar
  25. [25]
    Learner, E.E. (1981), “Sets of maximum likelihood estimates for regressions with errors in all the variables”, Department of Economics, Unviersity of California at Los Angeles. (Manuscript, August 1981.)Google Scholar
  26. [26]
    Pearson, K. (1901), “On lines and planes of closest fit to systems of points in space”, Philosophical Magazine, VI, 2, pp. 559–572.Google Scholar
  27. [27]
    Pearson, K. and Lee, A. (1903), “On the laws of inheritance in man. I. Inheritance of physical characters”, Biometrika, 2, pp. 357–462.Google Scholar
  28. [28]
    Reiersøl, O. (1941), “Confluence analysis by means of lag moments and other methods of confluence analysis”, Econometrica, 9, pp. 1–24.CrossRefGoogle Scholar
  29. [29]
    Schur, M. (1977), “Sigmund Freud: Leben und Sterben”, German translation of “Freud: Living and Dying”), Suhrkamp, 696 pagesGoogle Scholar
  30. [30]
    Sontag, E.D. and Rouchaleau, Y. (1976), “On discrete-time polynomial systems”, J. Nonlinear Analysis, 1, pp. 55–64..CrossRefGoogle Scholar
  31. [31]
    Spearman, C. (1904), “General intelligence objectively determined and measured”, American J. of Psychology, 15, pp. 201–293.CrossRefGoogle Scholar
  32. [32]
    Steiger, J.H. (1979), “Factor indeterminacy in the 1930’s and the 1970’s: some interesting parallels”, Psychometrika, 44, pp. 157–167.CrossRefGoogle Scholar
  33. [33]
    Theil, H. (1971), “Principles of Econometrics”, Wiley.Google Scholar
  34. [34]
    Willems, J.C. (1979), “System-theoretic models of physical systems”, Richerche di Automatica, 10, pp. 71–106.Google Scholar
  35. [35]
    Wold, H.O. (1969), “Mergers of economics and philosophy of science”, Synthèse, 20, pp. 427–482; see also “A key problem in the evolution of econometrics” in Economic Models, Estimation, and Risk Programming, Springer Lecture Notes in Operations Research and Mathematical Economics, no. 15, pp. 325–341.CrossRefGoogle Scholar
  36. [36]
    Yamamoto, Y. (1981), “Realization theory of infinite-dimensional linear systems”. Mathematical System Theory, 15, pp. 55–77 and 169–190.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1982

Authors and Affiliations

  • Rudolf E. Kalman
    • 1
  1. 1.Swiss Federal Institute of TechnologyZürich University of FloridaGainesvilleUSA

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