Subset selection with a generalized selection goal based on a loss function

P. Laan, van der, C. Eeden, van

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    Abstract

    Assume k (integer k = 2) populations are given. The associated independent random variables have continuous distribution functions with an unknown location parameter. The selection goal is to select a non-empty subset which contains the best, in the sense of largest location parameter, population with confidence level P* (k^{-1} <P* <1). In the present paper a generalized selection goal based on a general loss function is presented. This new loss function takes into account the difference, in parameter value, between the best population in the selected subset and the best of all k populations minus e (e \geq 0); it is zero if an e-best population is an element of the subset. An e-best population is any population with a parameter value within e of the value of the largest parameter. The generalized selection goal is thought to be of great value from an application point of view. The subset selection goal of Gupta is a special case of the introduced generalized selection goal. The special case of two normal populations is studied in detail.
    Original languageEnglish
    Place of PublicationEindhoven
    PublisherTechnische Universiteit Eindhoven
    Number of pages19
    Publication statusPublished - 1993

    Publication series

    NameMemorandum COSOR
    Volume9315
    ISSN (Print)0926-4493

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