  We study the well known difficult problem of prediction in measurement error
models. By targeting directly at the prediction interval instead of the point
prediction, we construct a prediction interval by providing estimators of both
the center and the length of the interval which achieves a pre-determined
prediction level. The constructing procedure requires a working model for the
distribution of the variable prone to error. If the working model is correct,
the prediction interval estimator obtains the smallest variability in terms of
assessing the true center and length. If the working model is incorrect, the
prediction interval estimation is still consistent. We further study how the
length of the prediction interval depends on the choice of the true prediction
interval center and provide guidance on obtaining minimal prediction interval
length. Numerical experiments are conducted to illustrate the performance and
we apply our method to predict concentration of Abeta1-12 in cerebrospinal
fluid in an Alzheimer's disease data.
