Robust estimation of generalized linear models with measurement errors

This paper considers consistent estimation of generalized linear models with covariate measurement errors. In contrast to the previous approach of assuming that measurement errors are normally distributed, we make no distributional assumptions on the latent variables or the measurement errors. Using the results of Li (J. Econometrics 110 (2002) 1) on the nonparametric identification and estimation of the distribution of the latent variables when replicate measurements are available, we propose to maximize the criterion based on an asymptotically corrected likelihood. We show that such an estimator is consistent. We also evaluate the finite sample performance of our estimator through a Monte Carlo study.