Odom-Maryon T, Langholz B, Niland J, Azen S
Department of Preventive Medicine, USC School of Medicine 90033.
Stat Med. 1991 Mar;10(3):473-85. doi: 10.1002/sim.4780100319.
In this paper we examine the efficiency of a generalization of the traditional normal linear (LDA) or quadratic (QDA) discriminant analysis. This procedure (the generalized discriminant analysis, GDA) replaces each normal density used in the traditional classification rule by a Fourier series density estimator which 'adjusts' the normal density if the data deviate markedly from normality (for example, heavily skewed or multimodal). We derive the GDA in both the univariate and multivariate situations. In a simulation study for the univariate situation, we evaluate the relative efficiency of the GDA. In addition, we demonstrate the performance of the GDA through a series of multivariate applications. We conclude that if the distributions of the data do not deviate markedly from normality, the GDA is as efficient as the LDA or QDA. On the other hand, if either of the distributions deviates from normality, then the GDA, which performs as a semiparametric discriminant procedure, is more efficient than the LDA or QDA.
在本文中，我们研究了传统正态线性判别分析（LDA）或二次判别分析（QDA）的一种推广形式的效率。此方法（广义判别分析，GDA）用傅里叶级数密度估计器替代了传统分类规则中使用的每个正态密度，若数据明显偏离正态性（例如，严重偏态或多峰），该估计器会对正态密度进行“调整”。我们在单变量和多变量情形下都推导出了GDA。在单变量情形的模拟研究中，我们评估了GDA的相对效率。此外，我们通过一系列多变量应用展示了GDA的性能。我们得出结论：如果数据分布没有明显偏离正态性，GDA与LDA或QDA效率相同。另一方面，如果其中任何一个分布偏离正态性，那么作为半参数判别方法的GDA比LDA或QDA更有效。
