On universally efficient estimation of the first order autoregressive parameter and universal data compression

Absfrucf -A universal nearly efficient estimator is proposed for the first order autoregressive (AR) model where the probability distribution of the driving noise is unknown. The proposed estimator has an intuitively appealing relation to universal data compression and to universal tests for randomness. Index Terms -asymptotically efficient estimation, universal estimation, Cramer-Rao bound, Fisher information, autoregressive process, universal coding.