Abstract
It is shown that the EVM in structural form is identifiable if serial correlation is present in the independent variables. Least Squares, Instrumental Variable and Maximum Likelihood techniques for the identification and estimation of serial correlations and other EVM parameters are given. The techniques used are based on State Vector Models, Kalman Filtering and Innovation representations. Generalizations to EVM involving multiple regressions and randomly time-varying coefficients are also discussed.
The work reported here was made possible through a grant from IIASA and through US Joint Services Contract No. N00014-67-A-0298-0006 to the Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. Wald, “The filtering of straight lines if both variables are subject to error”, The Annals of Mathematical Statistics 11 (1940) 284–300.
J. Neyman and E. Scott, “Consistent estimates based on partially consistent observations”, Econometrica 16 (1948) 1–32.
T. C. Koopmans and O. Reiersøl, “The identification of structural characteristics”, The Annals of Mathematical Statistics 21 (1950) 165–181.
J. Neyman, “Existence of a consistent estimate of the directional parameter in a linear structural relation between two variables”, The Annals of Mathematical Statistics, 22 (1951) 497–512.
J. Kiefer and J. Wolfowitz, “Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters”, The Annals of Mathematical Statistics 27 (1956) 887–906.
A. Madansky, “The fitting of straight lines when both variables are subject to error”, Journal of the American Statistical Association 54 (1959) 173–205.
M.E. Solari, “The maximum likelihood solution of the problem of estimating a linear functional relationship”, Journal of the Royal Statistical Society Ser. B, 31 (1969) 372–375.
A. Zellner, An introduction to Bayesian inference in econometrics (Wiley, New York, 1971).
P.A.P. Moran, “Estimating structural and functional relationships”, Journal of Multivariate Analysis 1 (1971) 232–255.
J.P. Florens, M. Mouchart and J.F. Richard, “Bayesian Inference in Error-in-Variables Models”, Journal of Multivariate Analysis 4 (1974) 419–452.
O. Reiersøl, “Identifiablity of a linear relation between variables which are subject to error”, Econometrica 18 (1950) 375–389.
A.E. Bryson and Y.C. Ho, Applied optimal control (Xerox Publishing Company, New York, 1969).
R.K. Mehra, “On line identification of linear dynamic systems with applications to Kalman filtering”, IEEE Transactions on Automatic Control AC-16 (1) (1971).
R.K. Mehra, “Identification in control and econometrics, similarities and differences”, Annals of Economic and Social Measurement (1974).
R.K. Mehra, “On the identification of variances and adaptive Kalman filtering”, IEEE Transactions on Automatic Control AC-15 (2) (1970).
J. Johnston, Econometric methods (McGraw-Hill, New York, 1963).
G.E.P. Box and G.M. Jenkins, Time series analysis forecasting and control (Holden Day, San Francisco, 1970).
N. Levinson, “The Wiener RMS criterion in filter design and prediction”, Appendix B of N. Wiener, Extrapolation, interpolation and smoothing of stationary time series (Wiley, New York, 1949).
J. Durbin, “The fitting of time series models,” Revue Inst. Int. Statistics 28 (1960) 233–244.
R.A. Wiggins and E.A. Robinson, “Recursive solution to the multichannel filtering problem,” Journal of Geophysics Research 70 (1965) 1885–1891.
R.K. Mehra and P.S. Krishnaprasad, “Fast recursive algorithms for parameter estimation”, to appear.
H. Akaike, “Canonical correlation analysis of time series and the use of an information criterion”, in: R.K. Mehra and D.G. Lainiotis, Eds, System Identification, advances and case studies (Marcel-Dekker, New York, 1976).
G.H. Golub, “Matrix decompositions and statistical calculations”, in: R.C. Milton and J.A. Nelda, Eds., Satistical Computation (Academic Press, New York, 1969).
K.J. Astrom, T. Bohlin and S. Wenmark, “Automatic construction of linear stochastic dynamic models for stationary industrial processes with random disturbances using operating records”, Rep. TP 18.150, IBM Nordic Laboratories, Lindingo, Sweden (1965).
L. Ljung, “On the consistency of prediction error identification methods”, in: R.K. Mehra and D.G. Lainiotis, Eds., Systems identification, advances and case studies (Marcel-Dekker, New York, 1975).
R.K. Mehra, “Identification of stochastic linear dynamic systems using Kalman filter representation”, AIAA Journal (1971).
N.K. Gupta and R.K. Mehra, “Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations”. IEEE Transactions on Automatic Control (1974).
F.C. Schweppe, Uncertain dynamic systems (Prentice Hall, New York, 1974).
R.K. Mehra, “A comparison of several nonlinear filters for re-entry vehicle tracking”, IEEE Transactions on Automatic Control (1971).
R.K. Mehra and P.S. Krishnaprasad, “A unified approach to structural estimation of distributed lags and stochastic differential equations”, Third NBER Conference on Stochastic Control, Washington, D.C. (1974).
R.K. Mehra and J.S. Tyler, “Case studies in aircraft parameter identification”, Third IFAC Conference on Identification, The Hague, Netherlands (June, 1973).
M.L. Brown, “Robust Line Estimation with errors in both variables”, Working Paper No. 83, Computer Research Center for Economics and Management Science, National Bureau of Economic Research, Inc., Cambridge, Mass, (May, 1975).
P. Whittle, “Tests of fit in time series”, Biometrika 39 (1952) 309–318.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1976 The Mathematical Programming Society
About this chapter
Cite this chapter
Mehra, R.K. (1976). Identification and estimation of the error-in-variables model (EVM) in structural form. In: Wets, R.J.B. (eds) Stochastic Systems: Modeling, Identification and Optimization, I. Mathematical Programming Studies, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120773
Download citation
DOI: https://doi.org/10.1007/BFb0120773
Received:
Revised:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00783-5
Online ISBN: 978-3-642-00784-2
eBook Packages: Springer Book Archive