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Regression with errors in variables: estimators based on third order moments

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  • K. van Montfort
  • A. Mooijaart
  • J. de Leeuw

Abstract

In this paper consistent and, in a well–defined sense, optimal moment–estimators of the regression coefficient in a simple regression model with errors in variables are derived. The asymptotic variance and other asymptotic properties of these estimators are given. As is known for a long time, serious estimation problems exist in this model. There are two ways out of this problem: using either additional assumptions or additional information in the data. A lot of attention has been paid to the use of additional assumptions. However, quite often this leads to rather unrealistic models. In this paper we use additional information in the data. That means here that, besides first and second order moments, third order moments are formulated as functions of the model parameters. Besides theoretical derivations a small study with generated data is discussed. This study shows that for samples larger than 50 the estimates we consider behave nicely.

Suggested Citation

  • K. van Montfort & A. Mooijaart & J. de Leeuw, 1987. "Regression with errors in variables: estimators based on third order moments," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 41(4), pages 223-238, December.
    • Handle: RePEc:bla:stanee:v:41:y:1987:i:4:p:223-238
    DOI: 10.1111/j.1467-9574.1987.tb01215.x
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    Cited by:

    1. Biørn, Erik, 2017. "Identification and Method of Moments Estimation in Polynomial Measurement Error Models," Memorandum 01/2017, Oslo University, Department of Economics.
    2. Paris, Quirino, 2014. "A Dual Least-Squares Estimator of the Errors-In-Variables Model Using Only First And Second Moments," Working Papers 181288, University of California, Davis, Department of Agricultural and Resource Economics.
    3. Erickson, Timothy & Jiang, Colin Huan & Whited, Toni M., 2014. "Minimum distance estimation of the errors-in-variables model using linear cumulant equations," Journal of Econometrics, Elsevier, vol. 183(2), pages 211-221.

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