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Asymptotic properties of covariate-adjusted regression with correlated errors. (English) Zbl 1160.62079
Summary: In covariate-adjusted regression (CAR), the response $$(Y)$$ and the predictors $$(X_r,r=1,\dots ,p)$$ are not observed directly. The estimation is based on $$n$$ independent observations $$\{\tilde Y_i,\tilde X_{ri}, U_i\}_{i=1}^n$$, where $$\tilde Y_i = \psi (U_i)Y_i,\tilde X_{ri} = \phi _r (U_i)X_{ri}$$ and $$\psi (\cdot)$$ and $$\{\phi _r(\cdot )\}^p_{r=1}$$ are unknown functions. We discuss the asymptotic properties of this method when the observations are correlated, as in regression models for repeated measurements.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F12 Asymptotic properties of parametric estimators 62M20 Inference from stochastic processes and prediction
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