On Rate of Convergence of Statistical Estimation of Stationary Ergodic Processes

Stationary ergodic processes with finite alphabets are approximated by finite memory processes based on an n-length realization of the process. Under the assumptions of summable continuity rate and non-nullness, a rate of convergence in
d̅
-distance is obtained, with explicit constants. Asymptotically, as
n
→ ∞, the result is near the optimum.