Local Linear Estimation for Spatiotemporal Models Based on Least Absolute Deviation
When the data contain outliers or come from population with heavy-tailed distributions, which appear very often in spatiotemporal data, the estimation methods based on least-squares (L2) method will not perform well. More robust estimation methods are required. In this article, we propose the local linear estimation for spatiotemporal models based on least absolute deviation (L1) and drive the asymptotic distributions of the L1-estimators under some mild conditions imposed on the spatiotemporal process. The simulation results for two examples, with outliers and heavy-tailed distribution, respectively, show that the L1-estimators perform better than the L2-estimators.