Sequential Estimation of the Largest Normal Mean When the Variance is Unknown
CORNELL UNIV ITHACA NY DEPT OF OPERATIONS RESEARCH
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Given n observations from each of k populations whose distributions differ by a location parameter, the value of the largest parameter is to be estimated using the largest value of the k sample means. It is desired to design a sampling rule which guarantees that the Mean Squared Error M.S.E. of the estimate does not exceed a given bound when the distributions have a common but unknown scale parameter. A sequential sampling scheme is devised based on an estimate of the scale parameter and a least favorable configuration of the location parameters. The sample size characteristics of the sampling plan studied under mild restrictions on the distributions involved. The M.S.E. of the resulting estimator is studied under the additional assumption of normality. A brief discussion is given of an alternate sequential plan which uses information in the sample regarding the configuration of the location parameters.
- Statistics and Probability