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 MissForest with Local Linear Forest and compare their performance with 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.

中文翻译：

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具有功能数据的现代多重插补

这项工作考虑了用稀疏和不规则采样的功能数据拟合功能模型的问题。它克服了最新方法的局限性，而这些方法在拟合更复杂的非线性模型时面临重大挑战。当前，除非随着样本量的增加，每条曲线的观察点数量增长得足够快，否则无法对这些模型中的许多模型进行一致的估计，而我们用数字表明，采用更现代的多种插补方法的改进方法通常可以产生更好的估计。我们还提出了一种新的估算方法，该方法将MissForest与本地线性林的思想相结合，并将其性能与PACE进行比较以及其他几种多元多重插补方法。这项工作是由对戒烟的纵向研究推动的，在该研究中，从宾夕法尼亚州立大学PaTH到Health的电子健康记录（EHR）允许收集大量数据，并进行高度可变的抽样。为了说明我们的方法，我们探讨了复发与舒张压之间的关系。我们还考虑了各种稀疏度不同的仿真方案，以验证我们的方法。