  We study the problem of estimating time-varying coefficients in ordinary
differential equations. Current theory only applies to the case when the
associated state variables are observed without measurement errors as presented
in \cite{chenwu08b,chenwu08}. The difficulty arises from the quadratic
functional of observations that one needs to deal with instead of the linear
functional that appears when state variables contain no measurement errors. We
derive the asymptotic bias and variance for the previously proposed two-step
estimators using quadratic regression functional theory.
