A Dynamic Interaction Semiparametric Function-on-Scalar Model

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 ageing and the socio-economic covariates, such as the number of hospital beds, physicians, nurses per 1,000 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. [ABSTRACT FROM AUTHOR] Copyright of Journal of the American Statistical Association is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)