An Optimal Two-Stage Procedure to Select the Best out of a Normal Population
Tóm tắt
In selecting a candidate with the largest expectation
$$\mu_{k}$$
(the best one) from a huge number a of candidates or let us say populations
$$P_{k}$$
with expectations
$$\mu_{k} t$$
, we can first select a smaller subset using Gupta’s procedure and then from this subset the best one by Bechhofer’s approach. A simulation experiment for normal distribution indicates when such a two-stage selection is optimal and preferred over using each procedure alone.
Tài liệu tham khảo
Bechhofer RE (1954) A single sample multiple decision procedure for ranking means of normal populations with known variances. Ann Math Stat 25:16–39
Gupta SS (1956) On a decision rule for a problem in ranking means, Mim. Ser., No 150, Univ. North Carolina
Gupta SS, Panchapakesan S (2002) Multiple decision problems: theory and methodology of selection and ranking populations. SIAM, University City
Miescke KJ, Rasch D (1996a) Special issue on 40 Years of statistical selection theory, Part I. J Stat Plan Inference 54(2)
Miescke KJ, Rasch D (1996b) Special Issue on 40 years of statistical selection theory, Part II. J Stat Plan Inference 54(3)
Rasch D, Schott D (2018) Mathematical statistics. Wiley, Oxford. ISBN 9781119385288