The Discrimination Subspace Model
针对两个总体p维正态随机向量，提出在差异仅存在于q维子空间的约束下进行判别的方法，介于线性与二次判别之间，通过降维和参数约束减少估计量，模拟和实例显示其误判率约为传统方法的一半。
Abstract For a p-variate normal random vector measured in two populations, we propose a method of discrimination under the constraint that all differences between the two populations occur in a subspace of dimension q < p. This method of classification is based on the discrimination subspace model, denoted by DSM(q), and is intermediate between linear and quadratic discrimination. It combines the ideas of dimension reduction and constraints on the parameter space, thus substantially reducing the number of parameters to be estimated. The maximum likelihood estimators of the model are presented, and the performance of DSM(q) versus quadratic and linear discrimination is assessed via simulation. It is generally shown that discrimination based on DSM(q) consistently yields noticeably lower expected actual error rates relative to the traditional methods. The method is illustrated with a real data example and is compared to linear and quadratic discrimination using a leave-one-out method. The example confirms the simulation results in that the DSM(q) discrimination function misclassified approximately one-half as many observations.