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Articles

Effect of measurement error size in linear heteroscedastic measurement error models

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Pages 5052-5081 | Received 08 Mar 2021, Accepted 09 Nov 2021, Published online: 13 Dec 2021

References

  • Boos, D. D., and L. A. Stefanski. 2013. Essential statistical inference: Theory and methods. New York: Springer.
  • Buonaccorsi, J. P. 2010. Measurement error: Models, methods, and applications. Boca Raton: Chapman and Hall/CRC.
  • Carroll, R. J. 1998. Measurement error in epidemiologic studies in encyclopedia of biostatistics. New York: Wiley, 2491–519.
  • Carroll, R. J., and D. Ruppert. 1996. The use and misuse of orthogonal regression in linear errors-in-variables models. The American Statistician 50 (1):1–6. doi:10.2307/2685035.
  • Carroll, R. J., D. Ruppert, L. A. Stefanski, and C. M. Crainiceanu. 2006. Measurement error in nonlinear models. A modern perspective. 2nd ed. London: Chapman & Hall.
  • Cheng, C.-L., and J. Riu. 2006. On estimating linear relationships when both variables are subject to heteroscedastic measurement errors. Technometrics 48 (4):511–9. doi:10.1198/004017006000000237.
  • Cheng, C. L., and H. Schneeweiss. 1998. Polynomial regression with errors in the variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 60 (1):189–99. doi:10.1111/1467-9868.00118.
  • Cheng, C. L., H. Schneeweiss, and M. Thamerus. 2000. A small sample estimator for a polynomial regression with errors in the variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 62 (4):699–709. doi:10.1111/1467-9868.00258.
  • Cheng, C.-L., and J.-R. Tsai. 2015. On interval estimation in linear relationships with heteroscedastic measurement errors in both axes. Chemometrics and Intelligent Laboratory Systems 142:276–84. doi:10.1016/j.chemolab.2015.01.011.
  • Cheng, C.-L., J.-R. Tsai, and H. Schneeweiss. 2019. Polynomial regression with heteroscedastic measurement errors in both axes: Estimation and hypothesis testing. Statistical Methods in Medical Research 28 (9):2681–2696. doi:10.1177/0962280218782715.
  • Cheng, C.-L., and J. W. Van Ness. 1999. Statistical regression with measurement error. London: Arnold.
  • de Castro, M., H. Bolfarine, and M. V. de Castilho. 2006. Consistent estimation and testing in comparing analytical bias models. Environmetrics 17 (2):167–82. doi:10.1002/env.760.
  • de Castro, M., M. Galea, and H. Bolfarine. 2008. Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors. Statistics in Medicine 27 (25):5217–34. doi:10.1002/sim.3343.
  • Dear, K. B. G., M. L. Puterman, and A. J. Dobson. 1997. Estimating correlations from epidemiological data in the presence of measurement error. Statistics in Medicine 16 (19):2177–89. doi:10.1002/(SICI)1097-0258(19971015)16:19<2177::AID-SIM646>3.0.CO;2-N.
  • Fuller, W. A. 1987. Measurement error models. New York: Wiley.
  • Gleser, L. 1987. J. Confidence intervals for the slope in a linear errors-in-variables models. In Advances in Multivariate Statistical Analysis, ed. K. Gupta, 85–109. Dordrecht: D. Reidel.
  • Kauermann, G., and R. J. Carrol. 2001. A note on the efficiency of sandwich covariance matrix estimation. Journal of the American Statistical Association. 96 (456):1387–96. doi:10.1198/016214501753382309.
  • Kelly, B. C. 2013. Measurement error models in astronomy. In Statistical Challenges in Modern Astronomy V. Lecture Notes in Statistics 209, eds. Eric D. Feigelson, G. Jogesh Babu, 147–62. New York: Springer.
  • Kulathinal, S. B., K. Kuulasmaa, and D. Gasbarra. 2002. Estimation of an errors-in-variables regression model when the variances of the measurement errors vary between the observations. Statistics in Medicine 21 (8):1089–101. doi:10.1002/sim.1062.
  • Nakamura, T. 1990. Corrected score function of errors-in-variables models: Methodology and applications to generalized linear models. Biometrika 77 (1):127–37. doi:10.1093/biomet/77.1.127.
  • Patriota, A. G., and H. Bolfarine. 2008. A heteroscedastic polynomial regression with measurement error in both axes. Shanksya 70-B:267–82.
  • Patriota, A. G., H. Bolfarine, and M. de Castro. 2009. A heteroscedastic structural errors-in-variables model with equation error. Statistical Methodology 6 (4):408–23. doi:10.1016/j.stamet.2009.02.003.
  • Sprent, P. 1966. A generalized least-squares approach to linear functional relationships. Journal of the Royal Statistical Society: Series B (Methodological) 28 (2):278–97. doi:10.1111/j.2517-6161.1966.tb00641.x.
  • Stefanski, L. A. 1989. Unbiased estimation of a nonlinear function a normal mean with application to measurement error models. Communications in Statistics - Theory and Methods 18 (12):4335–58. doi:10.1080/03610928908830159.
  • Zavala, A. Z., H. Bolfarine, and M. de Castro. 2007. Consistent estimation and testing in heteroscedastic polynomial errors-in-variables models. Annals of the Institute of Statistical Mathematics 59 (3):515–30. doi:10.1007/s10463-006-0069-1.
  • Zhang, X., Y. Ma, and R. J. Carroll. 2019. MALMEM: Model averaging in linear measurement error models. Journal of the Royal Statistical Society. Series B, Statistical Methodology 81 (4):763–79. doi:10.1111/rssb.12317.
  • Zhang, X., H. Wang, Y. Ma, and R. J. Carroll. 2017. Linear model selection when covariates contain errors. Journal of the American Statistical Association 112 (520):1553–61. doi:10.1080/01621459.2016.1219262.

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