Semiparametric Analysis of Isotonic Errors-in-Variables Regression Models with Missing Response

This article is concerned with the estimation problem in the semiparametric isotonic regression model when the covariates are measured with additive errors and the response is missing at random. An inverse marginal probability weighted imputation approach is developed to estimate the regression parameters and a least-square approach under monotone constraint is employed to estimate the functional component. We show that the proposed estimator of the regression parameter is root-n consistent and asymptotically normal and the isotonic estimator of the functional component, at a fixed point, is cubic root-n consistent. A simulation study is conducted to examine the finite-sample properties of the proposed estimators. A data set is used to demonstrate the proposed approach.