基于函数型数据的现代多重插补方法
Modern Multiple Imputation with Functional Data
AI总结：
针对稀疏不规则采样函数型数据拟合非线性模型的难题，提出结合MissForest与Local Linear Forest的新型多重插补方法，经真实戒烟纵向数据与多组模拟实验验证，其估计效果优于现有前沿方法。
摘要：
本研究针对稀疏且不规则采样的函数型数据拟合函数模型的问题，攻克了现有前沿方法在拟合更复杂非线性模型时面临重大挑战的局限。目前，除非每条曲线的观测点数量随样本量增长足够快，否则许多此类模型无法得到一致估计；而我们通过数值实验证明，结合更现代多重插补方法的改进方案通常能生成更优的估计结果。我们还提出一种将MissForest（缺失森林）与Local Linear Forest（局部线性森林）的思路相结合的新型插补方法，并将其性能与PACE（主成分分析通过条件期望）及其他多种多元多重插补方法进行对比。本研究的动因是一项关于戒烟的纵向研究，其中宾夕法尼亚州立大学PaTH to Health项目的电子健康记录（EHR）可采集大量采样高度不均的数据。为验证我们的方法，我们探究了复吸与舒张压之间的关系，同时还采用多种稀疏程度不同的模拟方案来验证所提方法的有效性。
英文摘要：
This work considers the problem of fitting functional models with sparsely and irregularly sampled functional data. It overcomes the limitations of the state-of-the-art methods, which face major challenges in the fitting of more complex non-linear models. Currently, many of these models cannot be consistently estimated unless the number of observed points per curve grows sufficiently quickly with the sample size, whereas, we show numerically that a modified approach with more modern multiple imputation methods can produce better estimates in general. We also propose a new imputation approach that combines the ideas of {\it MissForest} with {\it Local Linear Forest} and compare their performance with {\it PACE} and several other multivariate multiple imputation methods. This work is motivated by a longitudinal study on smoking cessation, in which the Electronic Health Records (EHR) from Penn State PaTH to Health allow for the collection of a great deal of data, with highly variable sampling. To illustrate our approach, we explore the relation between relapse and diastolic blood pressure. We also consider a variety of simulation schemes with varying levels of sparsity to validate our methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
