Diagnostics in Linear Discriminant Analysis
提出了线性判别分析中新的诊断度量，基于渐近分布理论构建临界值和Q-Q图来检测影响观测值，并指出回归诊断方法不适用于判别分析。
Abstract Some new diagnostic measures in discriminant analysis are proposed. They can be expressed in terms of the two fundamental influence statistics in discriminant analysis: d i 2 and ψ i . A theorem on the asymptotic distributions of the fundamental statistics is derived. Based on the theorem, the proposed measures can be shown to be asymptotically distributed as functions of independent chi-squared and standard normal random variables. Critical values and expected quantiles of the measures can then be constructed. Hence influential observations are detected using Q-Q plots and significance tests. Two measures have analogous forms in regression. The theorem is also useful for getting the asymptotic distributions of existing measures that are functions of d i 2 and ψ i . A comparison of the diagnostics in linear discriminant analysis, linear regression, and linear logistic regression (discriminant) analysis is made. Although discriminant coefficients can be determined under a regression model, regression diagnostic measures are shown to be inappropriate for detecting influential observations in linear discriminant analysis. The temptation of applying regression diagnostic measures in linear discriminant analysis must be resisted.