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A note on the simple structural regression model

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Abstract

In this paper we investigate some aspects like estimation and hypothesis testing in the simple structural regression model with measurement errors. Use is made of orthogonal parametrizations obtained in the literature. Emphasis is placed on some properties of the maximum likelihood estimators and also on the distribution of the likelihood ratio statistics.

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References

  • Abramowitz, M. and Stegun, I. A. (eds.) (1965). Handbook of Mathematical Functions, Dover, New York.

    Google Scholar 

  • Anderson, T. W. and Sawa, T. (1982). Exact and approximate distribution of maximum likelihood estimation of a slope coefficient, J. Roy. Statist. Soc. Ser. B, 44, 52–62.

    Google Scholar 

  • Arellano-Valle, R. B., Bolfarine, H. and Iglesias, P. L. (1995). A predictivistic interpretation of the t distribution, Test, 3 (2), 224–236.

    Google Scholar 

  • Bolfarine, H. and Cordani, L. K. (1993). Estimation of a structural linear regression model with a known reliability ratio, Ann. Inst. Statist. Math., 3, 531–540.

    Google Scholar 

  • Cordeiro, G. M. (1983). Improved likelihood ratio statistics for generalized linear models, J. Roy. Statist. Soc. Ser. B, 45, 404–413.

    Google Scholar 

  • Cox, D. R. and Reid, N. (1987). Parameter orthogonality and approximate conditional inference (with discussion). J. Roy. Statist. Soc. Ser. B, 49, 1–39.

    Google Scholar 

  • Fuller, W. A. (1987). Measurement Error Models, Wiley, New York.

    Google Scholar 

  • Kendall, M. and Stuart, A. (1979). The Advanced Theory of Statistics, Vol. 2, Griffin, London.

    Google Scholar 

  • Lawley, D. N. (1956). A general method for approximating to the distribution of the likelihood ratio criteria, Biometrika, 43, 295–303.

    Google Scholar 

  • Muirhead, R. J. (1982). Aspects of Multivariate Statistical Theory, Wiley, New York.

    Google Scholar 

  • Wong, M. Y. (1989). Likelihood estimation of a simple regression model when both variables have error, Biometrika, 76, 141–148.

    Google Scholar 

  • Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics, Wiley, New York.

    Google Scholar 

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Arellano-Valle, R.B., Bolfarine, H. A note on the simple structural regression model. Ann Inst Stat Math 48, 111–125 (1996). https://doi.org/10.1007/BF00049293

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  • DOI: https://doi.org/10.1007/BF00049293

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