Asymptotic bias calculations and corrections in segmented regression models with EIV

In this paper, the problem of a measurement error when estimating the breakpoint in a segmented linear regression model is discussed. It is shown that ignoring the measurement error can lead to a remarkably biased estimator. Different techniques for correcting this bias are presented and discussed with respect to their bias reduction: not only from a theoretical point of view, but also by simulation results. More detailed, we consider the regression calibration (RC) estimator, the recently proposed simulation and extrapolation approach, and a new estimator based on an exact bias correction. While the RC-estimator tends to an overcorrection with an increasing measurement error variance, the other estimators lead to a reasonable bias correction.