The Random-Effects Model in Discriminant Analysis
研究了随机效应模型下经典判别分析的特性，推导了马氏距离的分布，并给出了使用线性判别函数时误分类概率的期望表达式和界限。
Abstract In this article the characteristics of classical discriminant analysis under the random-effects model are investigated. Assuming that the elements within any randomly selected population are normally distributed with mean vector μ and common covariance matrix Σ, and that over different populations μ has a normal distribution with mean vector ξ and covariance matrix T, the distribution of the population-based and sample-based Mahalanobis distances between two different populations, as well as those between an observation and a randomly selected population, are derived. From these, expressions and bounds are derived for the expected probabilities of misclassification under classical discriminant analysis, applied to two- and multiple population problems respectively, when either the population-based or the sample-based linear discriminant functions are used.