We propose a new method to estimate a regression function based on the semiparametric density ratio model, which can be viewed as a generalized linear model with a canonical link function and an unspecified baseline distribution function. Under this model, the distribution of the observed data retains the same structure in the presence of selection-biased sampling or when the predictors are missing at random. In particular, in the latter case, the new method utilizes all the available information and does not need to specify the distribution of the predictors or the probability of observing the predictors. We establish large sample properties of the proposed regression estimators. Simulation studies demonstrate that the proposed estimators perform well in practical situations. Empirical data from the National Health and Nutrition Examination Survey are presented.

中文翻译：

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新的半参数回归方法在选择偏向抽样和缺失数据问题中的应用

我们提出了一种基于半参数密度比模型来估计回归函数的新方法，可以将其视为具有规范链接函数和未指定基线分布函数的广义线性模型。在该模型下，在存在选择偏向抽样或预测变量随机缺失的情况下，观测数据的分布保持相同的结构。特别是，在后一种情况下，新方法利用了所有可用信息，不需要指定预测变量的分布或观察预测变量的概率。我们建立了所提出的回归估计器的大样本属性。仿真研究表明，所提出的估计器在实际情况下表现良好。