A Note on Nonregular Likelihood Functions in Heteroscedastic Regression Models
研究了一类异方差回归模型的最大似然估计存在性问题，发现弱条件下似然函数在非重复观测点处奇异，导致无约束最大似然估计失效；另一类分散函数则需更强的线性独立条件才能避免似然无界。
The existence of maximum likelihood estimates for a class of heteroscedastic regression models is considered. For a given dispersion function we show that, under a weak condition, the likelihood is singular at points corresponding to nonreplicated observations, causing unrestricted maximum likelihood estimation to break down, whilst for an alternative class of dispersion functions we obtain a much stronger linear independence condition for the likelihood to be unbounded.