Central Limit Theorems for Conditional Markov Chains
Mathieu Sinn, Bei Chen · 2013
This paper studies Central Limit Theorems for real-valued functionals of Conditional Markov Chains. Using a classical result by Dobrushin (1956) for non-stationary Markov chains, a conditional Central Limit Theorem for fixed sequences of observations is estab-lished. The asymptotic variance can be es-timated by resampling the latent states con-ditional on the observations. If the condi-tional means themselves are asymptotically normally distributed, an unconditional Cen-tral Limit Theorem can be obtained. The methodology is used to construct a statistical hypothesis test which is applied to syntheti-cally generated environmental data. 1