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Replicated measurement error model under exact linear restrictions

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  • Sukhbir Singh
  • Kanchan Jain
  • Suresh Sharma

Abstract

We consider a replicated ultrastructural measurement error regression model where predictor variables are observed with error. It is assumed that some prior information regarding the regression coefficients is available in the form of exact linear restrictions. Three classes of estimators of regression coefficients are proposed. These estimators are shown to be consistent as well as satisfying the given restrictions. The asymptotic properties of unrestricted as well as restricted estimators are studied without imposing any distributional assumption on any random component of the model. A Monte Carlo simulations study is performed to assess the effect of sample size, replicates and non-normality on the estimators. Copyright Springer-Verlag 2014

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  • Sukhbir Singh & Kanchan Jain & Suresh Sharma, 2014. "Replicated measurement error model under exact linear restrictions," Statistical Papers, Springer, vol. 55(2), pages 253-274, May.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:2:p:253-274
    DOI: 10.1007/s00362-012-0469-7
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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. Chan, Lai K. & Mak, Tak K., 1979. "On the Maximum Likelihood estimation of a linear structural relationship when the intercept is known," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 304-313, June.
    3. 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.
    4. Klepper, Steven & Leamer, Edward E, 1984. "Consistent Sets of Estimates for Regressions with Errors in All Variables," Econometrica, Econometric Society, vol. 52(1), pages 163-183, January.
    5. Magne Thoresen & Petter Laake, 2003. "The Use of Replicates in Logistic Measurement Error Modelling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 625-636, September.
    6. 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.
    7. Aman Ullah & Shalabh & Debasri Mukherjee, 2001. "Consistent Estimation of Regression Coefficients in Replicated Data with Non-Normal Measurement Errors," Annals of Economics and Finance, Society for AEF, vol. 2(1), pages 249-264, May.
    8. Wang, Liqun, 1998. "Estimation of censored linear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 84(2), pages 383-400, June.
    9. 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.
    10. Devanarayan, Viswanath & Stefanski, Leonard A., 2002. "Empirical simulation extrapolation for measurement error models with replicate measurements," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 219-225, October.
    11. Shalabh, 1998. "Improved Estimation in Measurement Error Models Through Stein Rule Procedure," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 35-48, October.
    12. 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.
    13. 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.
    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. Jinhong You & Xian Zhou & Lixing Zhu & Bin Zhou, 2011. "Weighted denoised minimum distance estimation in a regression model with autocorrelated measurement errors," Statistical Papers, Springer, vol. 52(2), pages 263-286, May.
    16. 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.
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    Cited by:

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    3. Ai-Ai Liu & Han-Ying Liang, 2017. "Jackknife empirical likelihood of error variance in partially linear varying-coefficient errors-in-variables models," Statistical Papers, Springer, vol. 58(1), pages 95-122, March.

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