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Goodness of fit in restricted measurement error models

Author

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  • Cheng, C.-L.
  • Shalabh,
  • Garg, G.

Abstract

The restricted measurement error model is employed when certain study variables are not observable by direct measurement and if some information about the unknown regression coefficients is available a priori. In this study, we present a method for checking the goodness of fit in the restricted measurement error model. We obtain the goodness-of-fit statistics based on the concept of coefficient of determination and their asymptotic distributions are derived. The results of simulations are also presented to demonstrate the finite sample behaviour of the estimators.

Suggested Citation

  • Cheng, C.-L. & Shalabh, & Garg, G., 2016. "Goodness of fit in restricted measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 101-116.
  • Handle: RePEc:eee:jmvana:v:145:y:2016:i:c:p:101-116
    DOI: 10.1016/j.jmva.2015.12.005
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    References listed on IDEAS

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    1. Chi-Lun Cheng & Alexander Kukush, 2006. "Non-Existence of the First Moment of the Adjusted Least Squares Estimator in Multivariate Errors-in-Variables Model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(1), pages 41-46, August.
    2. Eshima, Nobuoki & Tabata, Minoru, 2011. "Three predictive power measures for generalized linear models: The entropy coefficient of determination, the entropy correlation coefficient and the regression correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3049-3058, November.
    3. Knight, John L., 1980. "The coefficient of determination and simultaneous equation systems," Journal of Econometrics, Elsevier, vol. 14(2), pages 265-270, October.
    4. Shalabh & Garg, Gaurav & Misra, Neeraj, 2009. "Use of prior information in the consistent estimation of regression coefficients in measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1498-1520, August.
    5. Srivastava, Anil K. & Shalabh, 1997. "Consistent estimation for the non-normal ultrastructural model," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 67-73, May.
    6. H. Schneeweiß, 1976. "Consistent estimation of a regression with errors in the variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 23(1), pages 101-115, December.
    7. Cheng, C.-L. & Shalabh, & Garg, G., 2014. "Coefficient of determination for multiple measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 137-152.
    8. Patriota, Alexandre G. & Bolfarine, Heleno & Arellano-Valle, Reinaldo B., 2011. "A multivariate ultrastructural errors-in-variables model with equation error," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 386-392, February.
    9. Ohtani, Kazuhiro & Hasegawa, Hikaru, 1993. "On Small Sample Properties of R2 in a Linear Regression Model with Multivariate t Errors and Proxy Variables," Econometric Theory, Cambridge University Press, vol. 9(3), pages 504-515, June.
    10. Cramer, J. S., 1987. "Mean and variance of R2 in small and moderate samples," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 253-266, July.
    11. Hilliard, Jimmy E. & Lloyd, William P., 1980. "Coefficient of determination in a simultaneous equation model: A pedagogic note," Journal of Business Research, Elsevier, vol. 8(1), pages 1-6, March.
    12. Liao J.G. & McGee D., 2003. "Adjusted Coefficients of Determination for Logistic Regression," The American Statistician, American Statistical Association, vol. 57, pages 161-165, August.
    13. McKean, Joseph W. & Sievers, Gerald L., 1987. "Coefficients of determination for least absolute deviation analysis," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 49-54, January.
    14. Shalabh & Gaurav Garg & Neeraj Misra, 2010. "Consistent estimation of regression coefficients in ultrastructural measurement error model using stochastic prior information," Statistical Papers, Springer, vol. 51(3), pages 717-748, September.
    15. Singh, Sukhbir & Jain, Kanchan & Sharma, Suresh, 2012. "Using stochastic prior information in consistent estimation of regression coefficients in replicated measurement error model," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 198-212.
    16. Shalabh, 2003. "Consistent estimation of coefficients in measurement error models with replicated observations," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 227-241, August.
    17. Ullah, Aman & Srivastava, Virendra K., 1994. "Moments of the ratio of quadratic forms in non-normal variables with econometric examples," Journal of Econometrics, Elsevier, vol. 62(2), pages 129-141, June.
    18. Shalabh & Garg, Gaurav & Misra, Neeraj, 2007. "Restricted regression estimation in measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1149-1166, October.
    19. Ohtani, Kazuhiro, 1994. "The density functions of R2 and , and their risk performance under asymmetric loss in misspecified linear regression models," Economic Modelling, Elsevier, vol. 11(4), pages 463-471, October.
    20. Jain, Kanchan & Singh, Sukhbir & Sharma, Suresh, 2011. "Restricted estimation in multivariate measurement error regression model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 264-280, February.
    21. Shalabh, 1998. "Improved Estimation in Measurement Error Models Through Stein Rule Procedure," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 35-48, October.
    22. Gleser, Leon Jay, 1993. "Estimators of slopes in linear errors-invariables regression models when the predictors have known reliability matrix," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 113-121, May.
    23. Srivastava, Anil K. & Shalabh, 1997. "Improved estimation of the slope parameter in a linear ultrastructural model when measurement errors are not necessarily normal," Journal of Econometrics, Elsevier, vol. 78(2), pages 153-157, June.
    24. Tjur, Tue, 2009. "Coefficients of Determination in Logistic Regression Models—A New Proposal: The Coefficient of Discrimination," The American Statistician, American Statistical Association, vol. 63(4), pages 366-372.
    25. Eshima, Nobuoki & Tabata, Minoru, 2010. "Entropy coefficient of determination for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1381-1389, May.
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