Screening in a Normal Model
当目标变量Y难以测量时，利用易测的相关变量X进行筛选，以提升成功个体比例。本文提出预测方法确定X的临界值，使保留个体的成功概率达标，并引入损失函数作为替代准则。
SUMMARY An individual is deemed ‘successful’ if the value of a certain measurement of interest Y lies in some given specification region. In situations in which Y is difficult to measure, the individuals may be screened using a correlated variable X which is easier to measure. The motivation behind screening is to try to increase the proportion of 'successes' by eliminating those individuals who are unlikely to be successful. Most approaches, except for very large sample situations, have incorporated the involved notions of tolerance regions. We present here a predictive approach to find the critical values of X for which the success probability for a retained future individual reaches a satisfactory level. A simple loss structure is also introduced to provide an alternative criterion for finding the critical values of the screening variable X. The methods are exemplified within the context of a bivariate normal model.