Cai Xiong, Cao Jiguo, Yan Xingyu, Zhao Peng
School of Statistics and Data Science, Nanjing Audit University, Nanjing, China.
Department of Statistics and Actuarial Science, Simon Fraser University, British Columbia, Canada.
Stat Med. 2025 Jun;44(13-14):e70140. doi: 10.1002/sim.70140.
We propose a new class of high-dimensional multiresponse partially functional linear regressions (MR-PFLRs) to investigate the relationship between scalar responses and a set of explanatory variables, which include both functional and scalar types. In this framework, both the dimensionality of the responses and the number of scalar covariates can diverge to infinity. To account for within-subject correlation, we develop a functional principal component analysis (FPCA)-based penalized weighted least squares estimation procedure. In this approach, the precision matrix is estimated using penalized likelihoods, and the regression coefficients are then estimated through the penalized weighted least squares method, with the precision matrix serving as the weight. This method allows for the simultaneous estimation of both functional and scalar regression coefficients, as well as the precision matrix, while identifying significant features. Under mild conditions, we establish the consistency, rates of convergence, and oracle properties of the proposed estimators. Simulation studies demonstrate the finite-sample performance of our estimation method. Additionally, the practical utility of the MR-PFLR model is showcased through an application to Alzheimer's disease neuroimaging initiative (ADNI) data.
我们提出了一类新的高维多响应部分函数线性回归（MR-PFLR），以研究标量响应与一组解释变量之间的关系，这些解释变量包括函数型和标量型。在此框架下，响应的维度和标量协变量的数量都可能趋于无穷大。为了考虑个体内部的相关性，我们开发了一种基于函数主成分分析（FPCA）的惩罚加权最小二乘估计方法。在这种方法中，使用惩罚似然估计精度矩阵，然后通过惩罚加权最小二乘法估计回归系数，精度矩阵作为权重。该方法允许同时估计函数型和标量回归系数以及精度矩阵，同时识别显著特征。在温和条件下，我们建立了所提出估计量的一致性、收敛速度和神谕性质。模拟研究展示了我们估计方法的有限样本性能。此外，通过将MR-PFLR模型应用于阿尔茨海默病神经影像倡议（ADNI）数据，展示了该模型的实际效用。
