On the Existence of Maximum Likelihood Estimates in Logistic Regression Models
研究逻辑回归模型中最大似然估计的存在性、唯一性和位置，通过数据点模式（完全分离、准完全分离和重叠）证明存在性定理，为识别频率表中对数线性模型的无限参数估计提供通用规则。
The problems of existence, uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature (Haberman, 1974, Chapter 2; Wedderburn, 1976; Silvapulle, 1981). For multinomial logistic regression models, we prove existence theorems by considering the possible patterns of data points, which fall into three mutually exclusive and exhaustive categories: complete separation, quasicomplete separation and overlap. Our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables.