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

The best variety or an almost best one? : a comparison of subset selection procedures

Given are k varieties. The best variety is defined as the variety with the largest average yield per plot of common unit size. An almost best or an e:-best variety is a variety with an average yield on a distance not larger than \epsilon (\geq 0) from the best variety. Subset selection is considered for selection of the best variety, but also for selection of an \epsilon-best variety. A comparison between these two selection goals is made by investigating the relative efficiency of subset selection of an \epsilon-best variety. An application is the field of variety testing is presented

Subset selection

Assume k (k \geq 2) populations are given. The associated independent random variables have continuous distribution functions differing only in their unknown location parameter. The statistical selection goal of subset selection is to select a non-empty subset which contains the best population with confidence level P*, with k^{-1} <P

Distribution theory for selection from logistic populations

Assume k (integer k \geq 2) independent populations \pi_1, \pi_2, ..., \pi_k are given. The associated independent random variables X_1, X_2, ..., X_k are Logistically distributed with unknown means \mu_1, \mu_2, ..., \mu_k, respectively, and common known variance. The goal is to select the best population, this is the population with the largest mean. Some distributional results are derived for subset selection as well as for the indifference zone approach. The probability of correct selection is determined. Exact and numerical results concerning the expected subset size are presented for the subset selection approach. Finally, some remarks are made for a generalized selection goal using subset selection. This goal is to select a non-empty subset of populations that contains at least one \epsilon-best (almost best) treatment with confidence level P*. For a set of populations an \epsilon-best reatment is defined as a treatment with location parameter on a distance less than or equal to \epsilon (\epsilon \geq 0) from the best population

The efficiency of subset selection of an epsilon-best uniform population relative to selection of the best one

Assume k (\geq 2) uniform populations are given on (\mu_i - ½, \mu_i + ½) with location parameter \mu_i \in R^1, i = 1, ..., k. The best population is defined as the population with the largest value of the location parameter. In \epsilon-best population (with \epsilon \geq 0) is a population with location parameter on a distance not larger than \epsilon from the largest value of \mu. It is possible to consider subset selection for an \epsilon-best population relative to subset selection for the best one. The relative efficiency is defined and computed in dependence of k and \epsilon for some values of the confidence level P* of selection