Central limit theorems for conditional Markov chains

Abstract

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.