From multivariate to functional data analysis: fundamentals, recent developments, and emerging areas

Modeling spatial-temporal variability of PM2.5 concentrations in Belt and Road Initiative (BRI) region via functional adaptive density approach

The rapid development of the Belt and Road Initiative (BRI) has led to severe air pollution dominated by PM2.5 concentrations which can cause a profound negative impact on human health and economic activity. This problem poses a critical environmental challenge to efficiently handling large-scale spatial-temporal PM2.5 data in this extended region. Functional data analysis (FDA) technique offers powerful tools that have the potential to enhance the analysis of spatial distributions and temporal dynamic changes in high-dimensional pollution data. However, modeling the spatial-temporal variability of PM2.5 concentrations by FDA remains unrevealed in the BRI region. To address this research gap, our study aimed to achieve two main objectives: first, to model the spatial-temporal dynamic variability of PM2.5 in 125 BRI nations (1998-2021), and second, to identify the underlying clusters behind the variations. We employed the recently developed functional adaptive density peak (FADP) clustering approach to solve the current problem. The proposed method is based on the joint use of functional principal components (FPCs) and functional cluster analyses. The main results are as follows: (i) The first three FPCs almost captured 99% of the total variations involving all valuable information on PM2.5 concentrations. (ii) PM2.5 pollution was highly concentrated in the developing countries (Pakistan, Bangladesh, and Nigeria) and the developed countries (Arabian Gulf countries: Qatar, United Arab Emirates, Bahrain, Saudi Arabia, Oman), and the least developed countries (Yemen and Chad). (iii) Three optimal clusters were identified and thus classified the PM2.5 into three distinct degrees of pollution: severe, moderate, and light. (iv) Cluster 1 had a severe pollution effect degree with a high rate of change, and it covered the Arabian Peninsula countries, African countries (Cameroon, Egypt, Gambia, Mali, Mauritania, Nigeria, Sudan, Senegal, Chad), Bangladesh, and Pakistan. (v) About 62 BRI countries belonged to cluster 2 showing a light pollution degree with annul average of less than 20 [Formula: see text]; this pointed out that the PM2.5 concentration remains stable in the cluster 2-related countries. The findings of this research would benefit governments and policymakers in preventing and controlling PM2.5 pollution exposure in BRI. Furthermore, this research could pay attention to sustainable development goals and the vision of the Green BRI policy.

Semiparametric function-on-function quantile regression model with dynamic single-index interactions

In this paper we propose a new semiparametric function-on-function quantile regression model with time-dynamic single-index interactions. Our model is very flexible in taking into account of the nonlinear time-dynamic interaction effects of the multivariate longitudinal/functional covariates on the longitudinal response, that most existing quantile regression models for longitudinal data are special cases of our proposed model. We propose to approximate the bivariate nonparametric coefficient functions by tensor product B-splines, and employ a check loss minimization approach to estimate the bivariate coefficient functions and the index parameter vector. Under some mild conditions, we establish the asymptotic normality of the estimated single-index coefficients using projection orthogonalization technique, and obtain the convergence rates of the estimated bivariate coefficient functions. Furthermore, we propose a score test to examine whether there exist interaction effects between the covariates. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and an empirical data analysis.

Multivariate Kalman filtering for spatio-temporal processes

An increasing interest in models for multivariate spatio-temporal processes has been noted in the last years. Some of these models are very flexible and can capture both marginal and cross spatial associations amongst the components of the multivariate process. In order to contribute to the statistical analysis of these models, this paper deals with the estimation and prediction of multivariate spatio-temporal processes by using multivariate state-space models. In this context, a multivariate spatio-temporal process is represented through the well-known Wold decomposition. Such an approach allows for an easy implementation of the Kalman filter to estimate linear temporal processes exhibiting both short and long range dependencies, together with a spatial correlation structure. We illustrate, through simulation experiments, that our method offers a good balance between statistical efficiency and computational complexity. Finally, we apply the method for the analysis of a bivariate dataset on average daily temperatures and maximum daily solar radiations from 21 meteorological stations located in a portion of south-central Chile.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00477-022-02266-3.