In the functional linear regression model, many methods have been proposed and studied to estimate the slope function while the functional predictor was observed in the entire domain. However, works on functional linear regression models with partially observed trajectories have received less attention. In this paper, to fill the literature gap we consider the scenario where individual functional predictor may be observed only on part of the domain. Depending on whether measurement error is presented in functional predictors, two methods are developed, one is based on linear functionals of the observed part of the trajectory and the other one uses conditional principal component scores. We establish the asymptotic properties of the two proposed methods. Finite sample simulations are conducted to verify their performance. Diffusion tensor imaging (DTI) data from Alzheimer's Disease Neuroimaging Initiative (ADNI) study is analyzed.
翻译:在功能线性回归模型中,提出并研究了许多方法来估计斜坡功能,而功能预测器则在整个领域观测到,然而,用部分观测到的轨迹进行功能线性回归模型的工程受到的注意较少,在本文件中,为填补文献空白,我们考虑了仅可在部分领域观测到单个功能预测器的设想方案,根据功能预测器中是否显示测量错误,开发了两种方法,一种方法以观察到的轨道部分的线性功能为基础,另一种方法使用有条件的主要组成部分分数。我们确定了两种拟议方法的无症状特性。我们进行了精度样本模拟,以核实其性能。分析了来自阿尔茨海默氏疾病神经成像倡议(ADNI)研究的聚合高光成像(DTI)数据。