Universal schemes for sequential decision from individual data sequences

Sequential decision algorithms are investigated, under a hmily of additive performance criteria, for individual data sequences, with varieus appliition areas in information theory and signal processing. Simple universal sequential schemes are known, under certain conditions, to approach optimality uniformly as fast as n-l log n, where n is the sample size. For the case of finite-alphabet observations, the class of schemes that can be implemented by bite-state machines (FSM's), is studied. It is shown that Markovian machines with d a e n t l y long memory exist that are asympboticaily nerrly as good as any given FSM (deterministic or W o m h I) for the purpose of sequential decision. For the continuous-valued observation case, a useful class of parametric schemes is discussed with special attention to the recursive least squares W) algorithm.