Asymptotic Normality of Nonparametric Kernel Regression Estimation for Missing at Random Functional Spatial Data

This study investigates the estimation of the regression function using the kernel method in the presence of missing at random responses, assuming spatial dependence, and complete observation of the functional regressor. We construct the asymptotic properties of the established estimator and derive the probability convergence (with rates) as well as the asymptotic normality of the estimator under certain weak conditions. Simulation studies are then presented to examine and show the performance of our proposed estimator. This is followed by examining a real data set to illustrate the suggested estimator's efficacy and demonstrate its superiority. The results show that the proposed estimator outperforms existing estimators as the number of missing at random data increases.

Automated summary

This study investigates the estimation of the regression function using the kernel method in the presence of missing at random responses, assuming spatial dependence, and complete observation of the functional regressor. The asymptotic properties of the estimator are constructed, and the probability convergence (with rates) as well as the asymptotic normality of the estimator are derived under certain weak conditions. Simulation studies and real data analysis demonstrate the superior performance of the proposed estimator especially when there are a large number of missing at random data.