Asymptotic properties of covariate-adjusted regression with correlated errors

In covariate-adjusted regression (CAR), the response (YY) and predictors (Xr,r=1,…,pXr,r=1,…,p) are not observed directly. Estimation is based on nn independent observations {Yĩ,X̃ri,Ui}i=1n, where Ỹi=ψ(Ui)Yi, X̃ri=ϕr(Ui)Xri and ψ(⋅)ψ(⋅) and {ϕr(⋅)}r=1p are unknown functions. In this paper, we discuss the asymptotic properties of this method when the observations are correlated, as in regression models for repeated measurements.