Predicted Bounds for Location Parameters of Selected Populations

Abstract

SYNOPTIC ABSTRACTAfter selecting t out of k populations (in terms of location) attempts are sometimes made to evaluate the selection process by forming estimates of the probability of correct selection. A more useful evaluation may be done by putting bounds (in a probability sense) on differences (in the location parameters) between (a) the worst selected and the best not selected .or (b) the best selected and the best not selected or (c) the average selected and the average not selected. For these quantities general results (for continuous distributions) are derived and particular results are found for normal distributions with unknown (but equal) variances.