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# Estimating a probability using finite memory

@article{Leighton1986EstimatingAP, title={Estimating a probability using finite memory}, author={Frank Thomson Leighton and Ronald L. Rivest}, journal={IEEE Trans. Information Theory}, year={1986}, volume={32}, pages={733-742} }

- Published 1986 in IEEE Trans. Information Theory
DOI:10.1109/TIT.1986.1057250

Let { X, }z 1 be a sequence of independent Bernoulli random variables with probability p that Xi = 1 and probability 4 = 1 p that X, = 0 for all i 2 1. Time-invariant finite-memory (i.e., finite-state) estimation procedures for the parameter p are considered which take X,, . as an input sequence. In particular, an n-state deterministic estimation procedure is described which can estimate p with mean-square error O(logn/n) and an n-state probabilistic estimation procedure which can estimate p… CONTINUE READING