Statistica Sinica 30 (2020), 955-975
Abstract: In this paper, we propose two estimating equation-based methods for estimating the regression parameter vector in a multiplicative regression model when a subset of covariates is subject to a measurement error, but replicate measurements of their surrogates are available. Both methods allow the number of replicate measurements to vary between subjects. No parametric assumption is imposed on the measurement error term or the true covariates, which are not observed in the data set. Under some regularity conditions, the asymptotic normality is proved for both proposed estimators. Furthermore, the estimators are compared theoretically when the distribution of the measurement error follows a normal distribution. Simulation studies are conducted to assess the performance of the proposed methods. A real-data analysis is used to illustrate our methods.
Key words and phrases: Estimating equations, measurement error, multiplicative regression model, product form, relative error, replicate measurement.