Flexible parametric approach to classical measurement error variance estimation without auxiliary data

Measurement error in the continuous covariates of a model generally yields bias in the estimators. It is a frequent problem in practice, and many correction procedures have been developed for different classes of models. However, in most cases, some information about the measurement error distribution is required. When neither validation nor auxiliary data (e.g., replicated measurements) are available, this specification turns out to be tricky. In this paper, we develop a flexible likelihood-based procedure to estimate the variance of classical additive error of Gaussian distribution, without additional information. The performance of this estimator is investigated both in an asymptotic way and through finite sample simulations. The usefulness of the obtained estimator when using the simulation extrapolation (SIMEX) algorithm, a widely used correction method, is then analyzed in the Cox proportional hazards model through other simulations. Finally, the whole procedure is illustrated on real data.