  Measurement error is a pervasive issue which renders the results of an
analysis unreliable. The measurement error literature contains numerous
correction techniques, which can be broadly divided into those which aim to
produce exactly consistent estimators, and those which are only approximately
consistent. While consistency is a desirable property, it is typically attained
only under specific model assumptions. Two techniques, regression calibration
and simulation extrapolation, are used frequently in a wide variety of
parametric and semiparametric settings. However, in many settings these methods
are only approximately consistent. We generalize these corrections, relaxing
assumptions placed on replicate measurements. Under regularity conditions, the
estimators are shown to be asymptotically normal, with a sandwich estimator for
the asymptotic variance. Through simulation, we demonstrate the improved
performance of the modified estimators, over the standard techniques, when
these assumptions are violated. We motivate these corrections using the
Framingham Heart Study, and apply the generalized techniques to an analysis of
these data.
