A model selection problem for the conditional probability function of the response variable $Y$ given the covariable vector $(X,Z)$ is considered under the case where $X$ is missing at random. And two novel model selection criteria are suggested. It is shown that the model selection by these two criteria is consistent and that the population parameter estimators, corresponding to the selected model, are also consistent and asymptotically normal. Extensive simulation studies are conducted to investigate the finite-sample performances of the proposed two criteria and a thorough comparison is made with some related model selection strategies. Moreover, two real data analyses are presented for illustrating the practical application of the proposed two criteria.

响应变量的条件概率函数的模型选择问题 $ÿ$ 给定协变量向量 $（X，ž）$ 被认为在以下情况下 $X$随机丢失。并提出了两种新颖的模型选择标准。结果表明，通过这两个标准进行的模型选择是一致的，并且与所选模型相对应的总体参数估计量也是一致的，并且渐近正常。进行了广泛的仿真研究，以研究所提出的两个标准的有限样本性能，并与一些相关的模型选择策略进行了全面的比较。此外，提出了两个真实的数据分析，以说明所提出的两个标准的实际应用。