标题： 通过惩罚逻辑回归比较两个样本 显示英文标题

标题： Comparing two samples by penalized logistic regression

摘要： 基于惩罚密度比模型的推断被提出并进行了研究。 所考虑的模型是通过假设两个未知密度的对数似然函数具有某种参数形式来定义的。 该模型已被扩展以涵盖多个样本问题，而其理论性质则通过大样本理论进行了研究。 密度比模型的一个主要应用是检验两个或更多分布是否相等。 我们通过论证惩罚最大经验似然估计量的均方误差小于普通最大似然估计量的均方误差，从而扩展了这些结果，尤其是在小样本情况下。 事实上，惩罚解决了估计量的存在性问题，并可以采用修正的Wald型检验统计量来检验两个分布的相等性。 一项有限的模拟研究进一步支持了这一理论。 显示英文摘要

摘要： Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log--likelihood function of two unknown densities is of some parametric form. The model has been extended to cover multiple samples problems while its theoretical properties have been investigated using large sample theory. A main application of the density ratio model is testing whether two, or more, distributions are equal. We extend these results by arguing that the penalized maximum empirical likelihood estimator has less mean square error than that of the ordinary maximum likelihood estimator, especially for small samples. In fact, penalization resolves any existence problems of estimators and a modified Wald type test statistic can be employed for testing equality of the two distributions. A limited simulation study supports further the theory.