标题： 样本分割作为具有物理活动评分应用的M估计量 显示英文标题

标题： Sample Splitting as an M-Estimator with Application to Physical Activity Scoring

摘要： 样本分割在统计应用中被广泛使用，包括在分类中的经典应用以及最近在模型选择后的推断。 受饮食、身体活动和健康研究中问题的启发，我们考虑了样本分割的新应用。 身体活动研究人员想要创建一个评分系统以快速评估身体活动水平。 该评分是通过一个大型队列研究创建的。 然后，使用相同的数据，该评分作为疾病或死亡风险模型中的协变量。 由于数据以这种方式被使用两次，拟合第二个模型的标准误差和置信区间无效。 为了进行正确的推断，可以使用样本分割。 一个人使用数据的一半来构建评分，然后在拟合另一部分数据的模型时使用该评分。 我们推导了估计量的极限分布。 一个明显的问题是如果进行多次样本分割会发生什么。 我们证明，随着样本分割次数的增加，多次样本分割的组合等价于求解一组估计方程。 显示英文摘要

摘要： Sample splitting is widely used in statistical applications, including classically in classification and more recently for inference post model selection. Motivating by problems in the study of diet, physical activity, and health, we consider a new application of sample splitting. Physical activity researchers wanted to create a scoring system to quickly assess physical activity levels. A score is created using a large cohort study. Then, using the same data, this score serves as a covariate in a model for the risk of disease or mortality. Since the data are used twice in this way, standard errors and confidence intervals from fitting the second model are not valid. To allow for proper inference, sample splitting can be used. One builds the score with a random half of the data and then uses the score when fitting a model to the other half of the data. We derive the limiting distribution of the estimators. An obvious question is what happens if multiple sample splits are performed. We show that as the number of sample splits increases, the combination of multiple sample splits is effectively equivalent to solving a set of estimating equations.