Optimal sequential sampling from two populations.

@article{Lai1984OptimalSS,
  title={Optimal sequential sampling from two populations.},
  author={T L Lai and Herbert Robbins},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1984},
  volume={81 4},
  pages={1284-6}
}
Given two statistical populations with unknown means, we consider the problem of sampling chi 1, chi 2, ... sequentially from these populations so as to achieve the greatest possible expected value of the sum Sn = chi 1 + ... + chi n. In particular, for normal populations, we obtain the optimal rule and study its properties when the average of the two population means is assumed known, and exhibit an asymptotically optimal rule without assuming any prior knowledge about the population means. 

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