Abstract

Motivated by recent work studying massive functional data, such as the COVID-19 data, we propose a new dynamic interaction semiparametric function-on-scalar (DISeF) model. The proposed model is useful to explore the dynamic interaction among a set of covariates and their effects on the functional response. The proposed model includes many important models investigated recently as special cases. By tensor product B-spline approximating the unknown bivariate coefficient functions, a three-step efficient estimation procedure is developed to iteratively estimate bivariate varying-coefficient functions, the vector of index parameters, and the covariance functions of random effects. We also establish the asymptotic properties of the estimators including the convergence rate and their asymptotic distributions. In addition, we develop a test statistic to check whether the dynamic interaction varies with time/spatial locations, and we prove the asymptotic normality of the test statistic. The finite sample performance of our proposed method and of the test statistic are investigated with several simulation studies. Our proposed DISeF model is also used to analyze the COVID-19 data and the ADNI data. In both applications, hypothesis testing shows that the bivariate varying-coefficient functions significantly vary with the index and the time/spatial locations. For instance, we find that the interaction effect of the population aging and the socio-economic covariates, such as the number of hospital beds, physicians, nurses per 1000 people and GDP per capita, on the COVID-19 mortality rate varies in different periods of the COVID-19 pandemic. The healthcare infrastructure index related to the COVID-19 mortality rate is also obtained for 141 countries estimated based on the proposed DISeF model.

摘要

受最近研究大量功能数据（例如 COVID-19 数据）的工作的启发，我们提出了一种新的动态交互半参数标量函数 (DISeF) 模型。所提出的模型有助于探索一组协变量之间的动态相互作用及其对功能反应的影响。所提出的模型包括许多最近作为特例研究的重要模型。通过张量积B样条逼近未知双变量系数函数，开发了一个三步高效估计程序来迭代估计双变量变系数函数、指标参数向量和随机效应的协方差函数。我们还建立了估计量的渐近特性，包括收敛率及其渐近分布。此外，我们开发了一个检验统计量来检查动态交互是否随时间/空间位置变化，我们证明了检验统计量的渐近正态性。我们提出的方法和测试统计的有限样本性能通过几个模拟研究进行了调查。我们提出的 DISeF 模型也用于分析 COVID-19 数据和 ADNI 数据。在这两个应用程序中，假设检验表明双变量变系数函数随索引和时间/空间位置显着变化。例如，我们发现人口老龄化与社会经济协变量（如每千人的病床数、医生、护士数和人均 GDP）对 COVID-19 死亡率的交互作用在不同时期有所不同COVID-19 大流行。