(Aalen, 1989) We consider the situation where there is just one covariate, X, that is measured with error, such that X = U +e where e is a zero-mean error term independent of U. We assume that the...

(Aalen, 1989) We consider the situation where there is just one covariate, X, that is measured with error, such that X = U +e where e is a zero-mean error term independent of U. We assume that the additive model holds with respect to the true covariate, such that

Assume that U and e are both normally distributed with variances
  respectively, and with the expectation of U equal to µ. Show that the model with respect to the observed covariate X is still an additive model and find the coefficients.

Chapter 5