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Details van artikel 9 van 28 gevonden artikelen
| Titel: |
Complete ranking procedures with appropriate loss functions |
| Auteur: |
Sobel, Marc J. |
| Verschenen in: |
Communications in statistics |
| Paginering: | Jaargang 19 (1990) nr. 12 pagina's 4525-4544 |
| Jaar: |
1990 |
| Inhoud: |
This paper treats the problem of comparing different evaluations of procedures which rank the variances of k normal populations. Procedures are evaluated on the basis of appropriate loss functions for a particular goal. The goal considered involves ranking the variances of k independent normal populations when the corresponding population means are unknown. The variances are ranked by selecting samples of size n from each population and using the sample variances to obtain the ranking. Our results extend those of various authors who looked at the narrower problem of evaluating the standard proceduv 3 associated with selecting the smallest of the population variances (see e.g.,P. Somerville (1975)). Different loss functions (both parametric and non-parametric) appropriate to the particular goal under consideration are proposed. Procedures are evaluated by the performance of their risk over a particular preference zone. The sample size n, the least favorable parametric configuration, and the maximum value of the risk are three quantities studied for each procedure. When k is small these quantities, calculated by numerical simulation, show which loss functions respond better and which respond worse to increases in sample size. Loss functions are compared with one another according to the extent of this response. Theoretical results are given for the case of asymptotically large k. It is shown that for certain cases the error incurred by using these asymptotic results is small when k is only moderately large. This work is an outgrowth of and extends that of J. Reeves and M.J. Sobel (1987) by comparing procedures on the basis of the sample size (perpopulation) required to obtain various bounds on the associated risk functions. New methodologies are developed to evaluate complete ranking procedures in different settings. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 9 van 28 gevonden artikelen
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