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
Highlights
The classical measurement error model is discussed in the context of parameter estimation of the simple linear regression
The classical simple linear regression model is making inferences in the functional relationship between the explanatory or independent variable X and the response or dependent variable Y from the observations (x; y): Sometimes, the explanatory variable cannot be directly observable or di¢ cult to observe for some situations
The basis of regression calibration (RC) is the replacement of the true explanatory variable X by the estimation of E(XjW ), which is denoted as E\ (XjW ) and will be called as RC function
Summary
The classical simple linear regression model is making inferences in the functional relationship between the explanatory or independent variable X and the response or dependent variable Y from the observations (x; y): Sometimes, the explanatory variable cannot be directly observable or di¢ cult to observe for some situations In these situations, a substitute variable W , generally called error-prone predictor, is observed instead of X that is, the random variable X is observed with measurement error U. Is the regression slope estimator biased and the ...tted line attenuated, and the data are noisier with increased error about the ...tted line. In this manuscript, two methods of correcting the attenuation, the regression calibration and simulation of extrapolation called SIMEX, are explained in more detail and compared in terms of the attenuation and variability. A real data example is given for an application to linear regression without intercept
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