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| Titel: |
On selecting the pareto-optimal subset of a class of populations |
| Auteur: |
Sobel, Marc |
| Verschenen in: |
Communications in statistics |
| Paginering: | Jaargang 21 (1992) nr. 4 pagina's 1085-1102 |
| Jaar: |
1992 |
| Inhoud: |
Let P be a class of k populations (with k known) each having an underlying multivariate normal distribution with unknown mean vector. We suppose that the mean (vector) value of each population can be represented by a vector parameter with p components and use the notation M to denote the set of all mean vectors for these k populations. Independent samples of size n are drawn from each population in P. We say that a subset G of P of vectors is δ*-Pareto-optimal if no vector in M, differing in at least one component from some mean vector μ corresponding to a population in G, has the property that each of its components is larger by at least δ* > 0 than the corresponding component of the vector μ In this paper we evaluate procedures devised to select the δ*-Pareto-Optimal subset of a class of populations according to the minimum probability of correct selection over a region of the parameter space which we call the preference zone. For small values of k, theoretical calculations are given to analyze how big a sample size n is needed to bound the minimum probability of correct selection below by a preassigned value P*. We usually take P* close to 1 (say .90 or .95), although theoretically we only need to have [image omitted] or Larger values of k, we construct an algorithm and also some computer simulation to show how this can be done. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 14 van 19 gevonden artikelen
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