In this paper, we propose a methodology essentially based on the Central Limit Theorem for Markov chains to monitor convergence of MCMC algorithms using actual outputs. Our methods are grounded on the fact that normality is a testable implication of sufficient mixing. The first control tool...

In this note, we establish the asymptotic distribution of the exponential tail estimator of extreme quantiles. We give sufficient conditions for the asymptotic normality and provide some illustrating examples.