Semiparametric estimation for measurement error models with validation data

Abstract

We consider regression problems where error-prone surrogates of true predictors are collected in a primary data set while accurate measurements of the predictors are available only in a relatively small validation data set. We propose a new class of semiparametric estimators for the regression coefficients based on expected estimating equations, where the relationship between the surrogates and the true predictors is modelled nonparametrically using a kernel smoother trained with the validation data. The new methods are developed under two different scenarios where the response variable is either observed or not observed in the validation data set. The proposed estimators have a natural connection with the fractional imputation method. They are consistent, asymptotically unbiased, and normal in both scenarios. Our simulation studies show that the proposed estimators are superior to competitors in terms of bias and mean squared error and are quite robust against the misspecification of the regression model and bandwidth selection. A real data application to the Korean Longitudinal Study of Aging is presented for illustration. The Canadian Journal of Statistics 45: 185-201; 2017 (c) 2017 Statistical Society of Canada