Theoretical analysis of a zero-redundancy estimator with a finite window for memoryless source

A zero-redundancy estimator is defined by a weighted sum of Krichevsky-Trofimov (KT) sequential probability estimators i.e., the minimax Bayes of the memoryless process, over all possible alphabets. This estimator is effective for non-binary sources whose alphabet is embedded in a larger alphabet. We propose a new weighting recursive computation. Next we use the estimator to construct a finite window predictor for lossless data compressor, and we show that its average redundancy for memoryless source has optimal 1st order asymptotics.