Regression calibration using response variables in linear models

Regression calibration is an easy way to improve estimation in errors-in-variables models. This method replaces missing covariates with estimates that are more accurate than surrogates. One might expect better estimation using response variables together with surrogates to estimate or predict missing values. However, the introducing of response variables generates bias in the estimating function. In this article, we use response variables to calibrate the missing covariates and provide an estimation method for the regression parameters in linear models. When errors in variables are small, we show that regression calibration using response variables outperforms the conventional regression calibration. A small simulation study comparing the performances of these methods in finite sample is provided.