Restricted Bayesian Inference for the Misspecified Random Repeated Measurements Model

This article presents a new technique for Bayesian inference in the random repeated measurements model. The fundamental idea underlying this work is the application of Bayesian inference to estimate the model parameters of interest. We then focus on theoretical results that allow the incorporation of linear constraints into the Bayesian estimator under model misspecification. It is essential to investigate the mathematical properties of the parameters; accordingly, this article also examines the asymptotic properties of the restricted Bayesian estimator for the misspecified repeated measurements model. It is shown that the Bayesian estimator of the second component of the parameter vector, under an underfitted model, is weakly consistent provided that certain conditions are satisfied. Moreover, in the presence of linear constraints, overfitting reduces the asymptotic efficiency of the Bayesian estimator of the second component of the parameter vector under certain conditions.