Polynomial regression and estimation function in the presence of multiplication measurement error, with application to nutrition

In this paper we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor. Consistent parameter estimates and their associated standard errors are derived. Two general methods are considered, with the methods differing in their assumptions about the distributions of the predictor and the measurement errors. Data from a nutrition study are analyzed using the methods. Finally, the results from a simulation study are presented and the performances of the methods compared.