ESTIMATION OF THE LINEAR-PLATEAU SEGMENTED REGRESSION-MODEL IN THE PRESENCE OF MEASUREMENT ERROR

It is well known that when the true values of the independent variable axe unobservable due to measurement error, the least squares estimator for a regression model is biased and inconsistent. When repeated observations on each x(i) are taken, consistent estimators for the linear-plateau model can be formed. The repeated observations are required to classify each observation to the appropriate line segment. Two cases of repeated observations are treated in detail. First, when a single value of y(i) is observed with the repeated observations of x(i) the least squares estimator using the mean of the repeated x(i) observations is consistent and asymptotically normal. Second, when repeated observations on the pair (x(i), y(i)) are taken the least squares estimator is inconsistent, but two consistent estimators are proposed: one that consistently estimates the bias of the least squares estimator and adjusts accordingly; the second is the least squares estimator using the mean of the repeated observations on each pair.