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Multicovariate-adjusted regression models. (English) Zbl 1431.62167
Summary: We introduce multicovariate-adjusted regression (MCAR), an adjustment method for regression analysis, where both the response $$(Y)$$ and predictors $$(X_{1}, \ldots , X_p)$$ are not directly observed. The available data have been contaminated by unknown functions of a set of observable distorting covariates, $$Z_{1}, \ldots , Z_s$$, in a multiplicative fashion. The proposed method substantially extends the current contaminated regression modelling capability, by allowing for multiple distorting covariate effects. MCAR is a flexible generalisation of the recently proposed covariate-adjusted regression method, an effective adjustment method in the presence of a single covariate, $$Z$$. For MCAR estimation, we establish a connection between the MCAR models and adaptive varying coefficient models. This connection leads to an adaptation of a hybrid backfitting estimation algorithm. Extensive simulations are used to study the performance and limitations of the proposed iterative estimation algorithm. In particular, the bias and mean square error of the proposed MCAR estimators are examined, relative to a baseline and a consistent benchmark estimator. The method is also illustrated with a Pima Indian diabetes data set, where the response and predictors are potentially contaminated by body mass index and triceps skin fold thickness. Both distorting covariates measure aspects of obesity, an important risk factor in type 2 diabetes.

##### MSC:
 62G08 Nonparametric regression and quantile regression 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 62P10 Applications of statistics to biology and medical sciences; meta analysis
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