Some Basic Results on the Extension of Quasi-Likelihood Based Measurement Error Correction to Multivariate and Flexible Structural Models

Quasi-score equations derived from corrected mean and variance
functions allow for consistent parameter estimation under
measurement error. However, the practical use of some approaches
relying on this general methodo\-logical principle was strongly
limited by the assumptions underlying them: only one covariate was
allowed to be measured with non-negligible error, and,
additionally, this covariate had to be conditionally independent of
the other covariates. This paper extends basic principles of this
method to multivariate and flexible models in a way that, on the
one hand, retains the neat statistical properties, but on the other
hand, manages to do without the restrictive assumptions needed up
to now.