We discuss a family of estimators for the entropy rate of a stationary ergodic process and prove their pointwise and mean consistency under a Doeblin-type mixing condition. The estimators are CesÃ roâ€¦ (More)

Let fXtg be a real-valued time series. The best nonlinear predictor of X0 given the infinite past X 1 1 , in the least squares sense, is equal to the conditional mean EfX0jX 1 1g. Previously, it hasâ€¦ (More)

The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known forâ€¦ (More)

Let M denote the distribution of an irreducible Markov chain supported by a finite directed graph 9, and let P,, denote the empirical type of the first n transitions. Csiszh, Cover, and Choi examinedâ€¦ (More)