Influential Observations in the Functional Measurement Error Model

Abstract

In this work we propose Bayesian measures to quantify the influence of observations on the structural parameters of the simple measurement error model (MEM). Different influence measures, like those based on q-divergence between posterior distributions and Bayes risk, are studied to evaluate the influence. A strategy based on the perturbation function and MCMC samples is used to compute these measures. The samples from the posterior distributions are obtained by using the Metropolis–Hastings algorithm and assuming specific proper prior distributions. The results are illustrated with an application to a real example modeled with MEM in the literature.

Keywords:

• MEM
• Influence measures
• Bayes risk
• q-divergence
• Perturbation function
• Metropolis–Hastings
• Gibbs sampling

Acknowledgement

This work has been supported by FONDECYT-Chile by grants 1050995 and 1030588.