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Inference for covariate adjusted regression via varying coefficient models. (English) Zbl 1095.62045
Summary: 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.

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62J05 Linear regression; mixed models
62E20 Asymptotic distribution theory in statistics
65C05 Monte Carlo methods
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