On Semiparametric EV Models with Serially Correlated Errors in Both Regression Models and Mismeasured Covariates

Abstract

Abstract. We consider inference for a semiparametric regression model where some covariates are measured with errors, and the errors in both the regression model and the mismeasured covariates are serially correlated. We propose a weighted estimating equations‐based estimator (WEEBE) for the regression coefficients. We show that the WEEBE is asymptotically more efficient than the estimators that neglect the serial correlations. This is an interesting new finding since earlier results in the statistical literature have shown that the weighted estimation is not as efficient as the unweighted estimation when the measurement errors and serially correlated errors of the regression models exist simultaneously (Biometrics, 49, 1993, 1262; Technometrics, 42, 2000, 137). The proposed WEEBE does not require undersmoothing the regressor functions in order to make it attain the root‐ n consistency. Simulation studies show that the proposed estimator has nice finite sample properties. A real data set is used to illustrate the proposed method.