By K. S. Fu (auth.), Professor King Sun Fu PhD (eds.)

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Math. Statist. 42,1075 (1971) M. E. HELLMAN: IEEE Trans. HELLMAN: IEEE Trans. Information Theory IT-1S, 429 (1972) F. SAMANIEGO: IEEE Trans. Information Theory IT-20, 387 (1974) P. F. LYNN, R.

73] applied time-varying rules for estimating the mean of a distribution. For Bernoulli observations WAGNER'S scheme is very close to optimal since its maximum absolute error is at most 11m with 2m states in memory. 74] establish that the optimal time-varying rule essentially stores a quantized version of the likelihood ratio, although the quantization is not of any simple form. Using detectors of the form given by MUISE and BooRSTYN will result in the fastest decay of error probability with increasing sample size.

The machine is restricted to make transitions only between adjacent states, and to move up on heads and down on tails. 102] examined the infinite sample, Gaussian estimation problem and showed that the problem can be reduced to a quantization problem. This result also applies to a larger class of infinite sample estimation problems. 103] has recently established some interesting results on the structure of optimal finite memory algorithms for testing k hypotheses, for k ~ 3. This problem remains unsolved, but SHUBERT was able to exhibit a counterexample to the natural conjecture that the optimal algorithm has a tree structure for its transition rule.

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