Abstract
In the context of sequential (point as well as interval) estimation, a general formulation of permutation-invariant stopping rules is considered. These stopping rules lead to savings in the ASN at the cost of some elevation of the associated risk—a phenomenon which may be attributed to the violation of the sufficiency principle. For the (point and interval) sequential estimation of the mean of a normal distribution, it is shown that such permutation-invariant stopping rules may lead to a substantial saving in the ASN with only a small increase in the associated risk.
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Work partially supported by (i) Office of Naval Research, Contract Number N00014-85-K-0548, and (ii) Office of Naval Research, Contract Number N00014-83-K-0387.
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Mukhopadhyay, N., Sen, P.K. & Sinha, B.K. Stopping rules, permutation invariance and sufficiency principle. Ann Inst Stat Math 41, 121–138 (1989). https://doi.org/10.1007/BF00049113
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DOI: https://doi.org/10.1007/BF00049113