Influential Observations In The Independent Student-T Measurement Error Model With Weak Nondifferential Error

As in regression analysis, inference in measurement error models (MEM) can be strongly modified by the inclusion or deletion of a small set of observations. Such observations are called influential data. In this work, we present different influence measures based on the Bayes risk and the q-divergence. These measures quantify the influence of a small subset of the data on the posterior distribution for the structural parameters of the independent Student-t MEM with weak nondifferential error. The advantage of the influence measures presented in this work is that we can compute them for any subset of data by using only one sample drawn from the posterior distribution. The samples from the posterior distributions are obtained through Gibbs sampler algorithm, assuming specific proper prior distributions. The Bayesian identifiability of the independent Student-t MEM with weak nondifferential error is also discussed. Finally, the results are illustrated with applications on two well-known real data sets.