Estimation methods for simple linear regression with measurement error: a real data application

Year 2017, Volume: 66 Issue: 2, 311 - 322, 01.08.2017

E.rukiye Dağalp İhsan Karabulut Fikri Öztürk

https://doi.org/10.1501/Commua1_0000000821

Abstract

The classical measurement error model is discussed in the context of parameter estimation of the simple linear regression. The attenuationeğect of measurement error on the parameter estimation is eliminated usingthe regression calibration and simulation extrapolation methods. The massdensity of pebbles population is investigated as a real data application. Themass and volume of a pebble are regarded an error-free and error-prone variables, respectively. The population mass density is considered to be the slopeparameter of the simple linear regression without intercept

Keywords

Classical measurement error model, consistent estimator, error invariables, linear regression, mass density, regression calibration, SIMEX method, M-estimation

References

• Carroll, R.J & Stefanski, L.A. , Approximate quasilikelihood estimation in models with sur- rogate predictors, Journal of the American Statistical Association, (1990), 85, pp. 652-663.
• Carroll, R.J., Ruppert, D., Stefanski, L.A.& Crainiceanu, C.M., Measurement Error in Non- linear Models, 2nd edn.Chapman & Hall/CRC 2006.
• Casella, G. & Berger, R. L. Statistical Inference, Duxbury Press, Belmont, 1990.
• Cook, J.R. & Stefanski, L.A., Simulation Extrapolation Estimation in Parametric Measure- ment Error Models, Journal of the American Statistical Association, (1994), 89, pp. 1314-1328.
• Fuller, W.A., Measurement Error Models, John Wiley and Sons, New York, 1987.
• Gleser, L.J., Improvements of the naive approach to estimation in nonlinear errors-in-variables regression models. In Statistical Analysis of Error Measurement Models and Application, P. J. Brown and W. A. Fuller, ed., Providence: American Mathematics Society, 1990.
• Ser*ing, R.J., Approximation Theorems of Mathematical Statistics, John Wiley and Sons, Singapore, 1980.
• Stefanski, L.A. & Cook, J.R., Simulation-Extrapolation: The Measurement Error, Journal of the American Statistical Association, (1995), 90, pp. 1247-1256. Current address : Rukiye E. Da¼galp (Corresponding author): Ankara University, Faculty of
• Sciences, Department of Statistics, 06100 Tando¼gan-Ankara/Turkey. E-mail address : [e-mail] Current address : ·Ihsan Karabulut:Ankara University, Faculty of Sciences, Department of Sta
• tistics, 06100 Tando¼gan-Ankara/Turkey. E-mail address : [e-mail] Current address : Fikri Öztürk:Ankara University, Faculty of Sciences, Department of Statis
• tics, 06100 Tando¼gan-Ankara/Turkey. E-mail address : [e-mail]