Theoretical Distributions of Optima for Univariate Discrimination of Random Data*
推导了单变量最优线性判别模型在随机连续数据下的理论分布，并给出样本量不超过30时的分布，为评估判别模型统计显著性提供了框架，有助于各学科研究者更广泛使用该方法。
ABSTRACT Optimal linear discriminant models maximize percentage accuracy for dichotomous classifications, but are rarely used because a theoretical framework that allows one to make valid statements about the statistical significance of the outcomes of such analyses does not exist. This paper describes an analytic solution for the theoretical distribution of optimal values for univariate optimal linear discriminant analysis, under the assumption that the data are random and continuous. We also present the theoretical distribution for sample sizes up to N = 30. The discovery of a statistical framework for evaluating the performance of optimal discriminant models should greatly increase their use by scientists in all disciplines.