Spatio-Functional Local Linear Asymmetric Least Square Regression Estimation: Application for Spatial Prediction of COVID-19 Propagation

Abstract

The problem of estimating the spatio-functional expectile regression for a given spatial mixing structure Xi,Yi∈F×R, when i∈ZN,N≥1 and F is a metric space, is investigated. We have proposed the M-estimation procedure to construct the Spatial Local Linear (SLL) estimator of the expectile regression function. The main contribution of this study is the establishment of the asymptotic properties of the SLL expectile regression estimator. Precisely, we establish the almost-complete convergence with rate. This result is proven under some mild conditions on the model in the mixing framework. The implementation of the SLL estimator is evaluated using an empirical investigation. A COVID-19 data application is performed, allowing this work to highlight the substantial superiority of the SLL-expectile over SLL-quantile in risk exploration.

Keywords

• functional data
• small ball probability
• local linear estimation
• Kolmogorov entropy
• complete convergence
• asymmetric least square regression