Empirical Convergence Rate of a Markov Transition Matrix

The convergence rate of a Markov transition matrix is governed by the second largest eigenvalue, where the first largest eigenvalue is unity, under general regularity conditions. Garren and Smith (2000) constructed confidence intervals on this second largest eigenvalue, based on asymptotic normality theory, and performed simulations, which were somewhat limited in scope due to the reduced computing power of that time period. Herein we focus on simulating coverage intervals, using the advanced computing power of our current time period. Thus, we compare our simulated coverage intervals to the theoretical confidence intervals from Garren and Smith (2000).