A predictive approach for the selection of a fixed number of good treatments

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Abstract

This paper offers a predictive approach for the selection of a fixed number (= t) of treatments from k treatments with the goal of controlling for predictive losses. For the ith treatment, independent observations Xij (j = 1,2,…,n) can be observed where Xij's are normally distributed N(θi; σ2). The ranked values of θi's and Xi's are θ(1) ≤… ≤θ X(k) and X[1] ≤… ≤X(k) and the selected subset S = {[k], [k – 1],…, [k - t + 1]} will be considered. This paper distinguishes between two types of loss functions. A type I loss function associated with a selected subset S is the loss in utility from the selector's view point and is a function of θi with i εS. A type I1 loss function associated with S measures the unfairness in the selection from candidates' viewpoint and is a function of θi with i ε S. This paper shows that under mild assumptions on the loss functions S is optimal and provides the necessary formulae for choosing n so that the two types of loss can be controlled individually or sinlultaneously with a high probability. Predictive bounds for the losses are provided. Numerical examples support the usefulness of the predictive approach over the design of experiment approach. Copyright © 1994 Taylor & Francis Group, LLC. All rights reserved.
Original languageEnglish
Pages (from-to)2469-2492
JournalCommunications in Statistics - Theory and Methods
Volume23
Issue number9
DOIs
Publication statusPublished - 1994

Citation

Lam, K., & Yu, P. L. H. (1994). A predictive approach for the selection of a fixed number of good treatments. Communications in Statistics - Theory and Methods, 23(9), 2469-2492. doi: 10.1080/03610929408831398

Keywords

  • Ranking and selection
  • Predictive approach
  • Correct selection
  • Predictive bounds
  • Simultaneous control

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