  We consider covariate adjusted regression (CAR), a regression method for
situations where predictors and response are observed after being distorted by
a multiplicative factor. The distorting factors are unknown functions of an
observable covariate, where one specific distorting function is associated with
each predictor or response. The dependence of both response and predictors on
the same confounding covariate may alter the underlying regression relation
between undistorted but unobserved predictors and response. We consider a class
of highly flexible adjustment methods for parameter estimation in the
underlying regression model, which is the model of interest. Asymptotic
normality of the estimates is obtained by establishing a connection to varying
coefficient models. These distribution results combined with proposed
consistent estimates of the asymptotic variance are used for the construction
of asymptotic confidence intervals for the regression coefficients. The
proposed approach is illustrated with data on serum creatinine, and finite
sample properties of the proposed procedures are investigated through a
simulation study.
