AI 中文总结
研究线性模型均值误设下模型有用性问题，提出利用有用性指数通过均值模型在个体观测间共享信息的方法，定义新估计量并与詹姆斯 - 斯坦估计量联系，还给出有用性指数数据相关估计，通过个人追踪器数据分析展示方法实用价值。
AI 中文摘要
几乎所有模型都是错误的，均值模型的有用性常被视作其使用的充分理由。然而在实践中，当均值模型拟合不完美时，标准统计理论会失效，限制了其有用性。这种拟合与有用性之间的矛盾源于模型拟合的二分法：模型非对即错。受线性回归框架启发，我们提出一种新观点，在不假定均值模型对错的情况下利用其有用性。我们定义了一个新的模型有用性指数，并通过均值模型在个体观测间共享信息。结果得到一个各结果均值的估计量，它将个体均值向共享均值模型收缩，收缩程度由该有用性指数决定。我们将我们的估计量与詹姆斯 - 斯坦估计量建立联系，并确定我们的个体均值估计量何时以及如何比基于模型和非基于模型的替代方法产生更有效的推断。我们还提出了一个与数据相关的有用性指数估计量，它在统计直觉和效率考量之间取得平衡。我们在个人追踪器数据分析中展示了我们方法的实用价值。
英文摘要
As almost all models are wrong, a mean model's usefulness is often accepted as sufficient justification for its use. In practice, however, standard statistical theory breaks when the mean model fit is imperfect, limiting this usefulness. This tension between fit and usefulness arises from a dichotomization of model fit: the model is either right or it is wrong. Motivated by the linear regression framework, we propose an alternative viewpoint that leverages the mean model's usefulness without assuming it is right or wrong. We define a new model usefulness index and use it to share information across individual observations through the mean model. The result is an estimator of each outcome's mean that shrinks individualized means towards the shared mean model, with the degree of shrinkage governed by this usefulness index. We draw connections between our estimator and the James-Stein estimator and establish when and how our estimators of the individualized means yield more efficient inference than model-based and non-model-based alternatives. We also propose a data-dependent estimate of the usefulness index that balances statistical intuition with efficiency considerations. We illustrate our method's practical value in an analysis of personal tracker data.
Comments21 pages, 6 figures, 2 tables
