Statistical learning with ranked set samples has shown promising results in estimating various population parameters. Despite the vast literature on rank-based statistical learning methodologies, very little effort has been devoted to studying regression analysis with such samples. A pressing issue is how to incorporate the rank information of ranked set samples into the analysis. We propose two methodologies based on a weighted least squares approach and multilevel modeling to better incorporate the rank information of such samples into the estimation and prediction processes of regression-type models. Our approaches reveal significant improvements in both estimation and prediction problems over already existing methods in the literature and the corresponding ones with simple random samples. We study the robustness of our methods with respect to the misspecification of the distribution of the error terms. Also, we show that rank-based regression models can effectively predict simple random test data by assigning ranks to them a posteriori using judgment poststratification. Theoretical results are augmented with simulations and an osteoporosis study based on a real data set from the Bone Mineral Density (BMD) program of Manitoba to estimate the BMD level of patients using easy to obtain covariates.

中文翻译：

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再看使用排序集样本进行回归分析并应用于骨质疏松症研究

使用排序集样本的统计学习在估计各种总体参数方面显示出可喜的结果。尽管有大量关于基于排名的统计学习方法的文献，但很少有人致力于研究此类样本的回归分析。一个紧迫的问题是如何将排名集样本的排名信息纳入分析。我们提出了两种基于加权最小二乘法和多级建模的方法，以更好地将此类样本的秩信息纳入回归型模型的估计和预测过程。我们的方法揭示了在估计和预测问题上比文献中已有的方法和具有简单随机样本的相应方法有显着改进。我们研究了我们的方法在误差项分布的错误指定方面的稳健性。此外，我们还表明，基于等级的回归模型可以通过使用判断后分层为后验分配等级来有效地预测简单的随机测试数据。理论结果通过模拟和基于马尼托巴骨矿物质密度 (BMD) 计划的真实数据集的骨质疏松症研究得到增强，以使用易于获得的协变量来估计患者的 BMD 水平。