Estimation for spatial semi-functional partial linear regression model with missing response at random

The aim of this article is to study a semi-functional partial linear regression model (SFPLR) for spatial data with responses missing at random (MAR). The estimators are constructed using the kernel method, and some asymptotic properties, such as the probability convergence rates of the nonparametric component and the asymptotic distribution of the parametric and nonparametric components, are established under certain conditions. Next, the performance and superiority of these estimators are presented and examined through a study on simulated data, comparing our semi-functional partially linear model with the MAR estimator to the semi-functional partially linear model with the full-case estimator, and the functional nonparametric regression model estimator with MAR. The results indicate that the proposed estimators outperform traditional estimators as the amount of randomly missing data increases. Additionally, a study is conducted on real data regarding the modeling of pollution levels using our model, incorporating covariates such as average daily temperature as a functional variable, alongside maximum daily mixing height, total daily precipitation, and daily primary aerosol emission rates as explanatory variables.