Subset selection for an epsilon-best population : efficiency results

An almost best or an \epsilon-best population is defined as a population with location parameter on a distance not larger than \epsilon (\geq 0) from the best population (with largest value of the location parameter). For the subset selection tables with the relative efficiency of selecting an \epsilon-best population relative to selecting the best population are given. Results are presented for confidence level P* = 0.50, 0.80, 0.90, 0.95 and 0.99; the number of populations k =2(1)15(5)50(10)100(50)300(100)500(250)2000, and \epsilon = 0.2, 0.5, 1.0, 1.5 and 2.0, where P* is the minimal probability of correct selection

Subset selection for an epsilon-best population : efficiency results

An almost best or an \epsilon-best population is defined as a population with location parameter on a distance not larger than \epsilon (\geq 0) from the best population (with largest value of the location parameter). For the subset selection tables with the relative efficiency of selecting an \epsilon-best population relative to selecting the best population are given. Results are presented for confidence level P* = 0.50, 0.80, 0.90, 0.95 and 0.99; the number of populations k =2(1)15(5)50(10)100(50)300(100)500(250)2000, and \epsilon = 0.2, 0.5, 1.0, 1.5 and 2.0, where P* is the minimal probability of correct selection

Experiments : design, parametric and nonparametric analysis, and selection

Some general remarks for experimental designs are made. The general statistical methodology of analysis for some special designs is considered. Statistical tests for some specific designs under Normality assumption are indicated. Moreover, nonparametric statistical analyses for some special designs are given. The method of determining the number of observations needed in an experiment is considered in the Normal as well as in the nonparametric situation. Finally, the special topic of designing an experiment in order to select the best out of k(\geq 2) treatments is considered

Subset selection : robustness and imprecise selection

Assume k (integer k \qeq 2) independent populations are given. The associated independent random variables have distributions with an unknown location parameter. The goal is to select the best population, this is the population with largest value of the location parameter. First, this paper reviews some distributional and robustness results for Subset Selection from Normal populations. Special attention is given to the probability of correct selection. Secondly, some distributional results are given. Explicit expressions for expectation and variance of the subset size using Subset Selection are presented. Finally, some remarks are made concerning a generalized selection goal using Subset Selection. Instead of selecting precisely the best population, an imprecise selection can be applied, that is selection of a population in the neighbourhood of the best population. The generalized Subset Selection goal is to select a non-empty subset of populations that contains at least one almost best population with a certain confidence level. For a collection of populations with an unknown location parameter an almost best population, or more accurately an \epsilon-best population, is defined as a population with location parameter on a distance less than or equal to \epsilon (with \epsilon \geq 0) from the maximal value of the location parameter for all populations. The selection of an almost best population is compared with the selection of the best one from an application point of view. Some efficiency results are presented

Two-stage selection procedures with attention to screening

Some literature concerning two-stage selection procedures is given. In general, the problem of selecting the Normal population with largest mean from k(\geq 2) Normal populations with a common variance is considered. Special attention is drawn to two-stage procedures with screening for selecting the best. Such a procedure consists of a combination of the subset selection approach and the indifference zone approach. The first stage is used for eliminating bad populations and the second stage is used to indicate the best population from the remaining part

Subset selection : robustness and imprecise selection

Assume k (integer k \qeq 2) independent populations are given. The associated independent random variables have distributions with an unknown location parameter. The goal is to select the best population, this is the population with largest value of the location parameter. First, this paper reviews some distributional and robustness results for Subset Selection from Normal populations. Special attention is given to the probability of correct selection. Secondly, some distributional results are given. Explicit expressions for expectation and variance of the subset size using Subset Selection are presented. Finally, some remarks are made concerning a generalized selection goal using Subset Selection. Instead of selecting precisely the best population, an imprecise selection can be applied, that is selection of a population in the neighbourhood of the best population. The generalized Subset Selection goal is to select a non-empty subset of populations that contains at least one almost best population with a certain confidence level. For a collection of populations with an unknown location parameter an almost best population, or more accurately an \epsilon-best population, is defined as a population with location parameter on a distance less than or equal to \epsilon (with \epsilon \geq 0) from the maximal value of the location parameter for all populations. The selection of an almost best population is compared with the selection of the best one from an application point of view. Some efficiency results are presented