A Note on Maximum Likelihood Estimation for Regression Models Using Grouped Data
研究分组或删失数据回归模型的参数估计，证明通过简单重参数化可使某些常用分布的对数似然函数关于变换后的参数是凹的，从而保证最大似然估计的存在性和唯一性，并建议对常用算法做微小调整。
Summary The estimation of parameters for a class of regression models using grouped or censored data is considered. It is shown that with a simple reparameterization some commonly used distributions, such as the normal and extreme value, result in a log-likelihood which is concave with respect to the transformed parameters. Apart from its theoretical implications for the existence and uniqueness of maximum likelihood estimates, this result suggests minor changes to some commonly used algorithms for maximum likelihood estimation from grouped data. Two simple examples are given.