泛函线性模型的不确定性估计
Uncertainty Estimation in Functional Linear Models
摘要：
函数数据分析在许多科学应用中被证明是有用的。物理过程被观察为曲线，并且通常由于多个受试者而观察到多个曲线，从而提供统计意义上的重复。最近的文献发展了几种技术，用于记录曲线和相关的模型估计。然而，很少有研究统计推断，特别是不确定性估计。在这篇文章中，我们考虑函数线性混合建模方法来组合几个曲线。当使用泛函线性混合模型进行预测时，我们集中测量不确定度。虽然测量的不确定性是最重要的兴趣在任何统计预测，有没有封闭的形式表达功能混合效应模型。在许多实际应用中，只能观察到有限数量的曲线。在这种情况下，重要的是要评估任何有效的统计报表的错误率。我们推导出理论上有效的近似的不确定性测量是合适的，随着修改后的估计技术。我们通过数值例子说明我们的方法，并与其他现有文献进行适当的比较。我们的方法是计算简单，往往优于其他方法。
英文摘要：
Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense. The recent literature develops several techniques for registering the curves and associated model estimation. However, very little has been investigated for statistical inference, specifically uncertainty estimation. In this article, we consider functional linear mixed modeling approach to combine several curves. We concentrate measuring uncertainty when the functional linear mixed models are used for prediction. Although measuring the uncertainty is paramount interest in any statistical prediction, there is no closed form expression available for functional mixed effects models. In many real life applications only a finite number of curves can be observed. In such situations it is important to asses the error rate for any valid statistical statement. We derive theoretically valid approximation of uncertainty measurements that are suitable along with modified estimation techniques. We illustrate our methods by numerical examples and compared with other existing literature as appropriate. Our method is computationally simple and often outperforms the other methods.
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