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Estimating structural and functional relationships

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  • Moran, P. A. P.

Abstract

This paper surveys the problem of estimating a linear relationship between variables which are observed with error. These are either fixed variables (functional relationship) or random variables (structural relationship). After considering various conditions for identifiability, estimation methods are surveyed in various cases when additional information is available, including Wald's method, the use of instrumental variates, and the case of more than two variables. The paper concludes with a list of unsolved problems.

Suggested Citation

  • Moran, P. A. P., 1971. "Estimating structural and functional relationships," Journal of Multivariate Analysis, Elsevier, vol. 1(2), pages 232-255, June.
    • Handle: RePEc:eee:jmvana:v:1:y:1971:i:2:p:232-255
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    Citations

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    Cited by:

    1. Paul A. Bekker & Jan van der Ploeg, 2000. "Instrumental Variable Estimation Based on Grouped Data," Econometric Society World Congress 2000 Contributed Papers 1862, Econometric Society.
    2. Tak Mak & Fassil Nebebe, 2009. "Numerical approximation of conditional asymptotic variances using Monte Carlo simulation," Computational Statistics, Springer, vol. 24(2), pages 333-344, May.
    3. J. Healy, 1979. "On kristof's test for a linear relation between true scores of two measures," Psychometrika, Springer;The Psychometric Society, vol. 44(2), pages 235-238, June.
    4. Shalabh, 1998. "Improved Estimation in Measurement Error Models Through Stein Rule Procedure," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 35-48, October.
    5. A. Ronner & A. Steerneman, 1985. "The occurrence of outliers in the explanatory variable considered in an errors-in-variables framework," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 97-107, December.
    6. Li, Junbao & Shi, Zhanzhong & He, Chengying & Lv, Chengshuang, 2023. "Peer effects on corporate R&D investment policies: A spatial panel model approach," Journal of Business Research, Elsevier, vol. 158(C).
    7. Kamal C. Chanda, 1995. "Large Sample Analysis Of Autoregressive Moving‐Average Models With Errors In Variables," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 1-15, January.
    8. Correndo, Adrian A. & Hefley, Trevor J. & Holzworth, Dean P. & Ciampitti, Ignacio A., 2021. "Revisiting linear regression to test agreement in continuous predicted-observed datasets," Agricultural Systems, Elsevier, vol. 192(C).
    9. R. Ketellapper & A. Ronner, 1984. "Are robust estimation methods useful in the structural errors-in-variables model?," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 31(1), pages 33-41, December.
    10. Willasen, Y., 1998. "Deriving Bounds on the Structural Vector when the Measurement Errors are Correlated: An Elaboration of the Frisch/Reiersol Approach," Memorandum 06/1998, Oslo University, Department of Economics.
    11. Longcheen Huwang & Y. Steve Huang & Yi-Hua Tina Wang, 2009. "Uniformly robust tests in errors-in-variables models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 789-810, December.

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