Robust linear regression in replicated measurement error models

We propose robust and bounded influence methods for linear regression when some of the predictors are measured with error. We address the important special case that the surrogate predictors are replicated, and that the measurement errors in response and predictors are correlated. The robust methods proposed are variants of the so-called Mallows class of estimates. The resulting estimators are easily computed and have a simple asymptotic theory. An example is used to illustrate the results.