Principal component empirical likelihood method for non-panel spatial data models

While empirical likelihood methods offer the advantages of being distribution-free and data-adaptive, their conventional implementations deteriorate significantly under high-dimensional moment constraints. This limitation poses substantial challenges for practical applications in spatial autoregressive models with autoregressive disturbances (SARSAR models). To overcome this limitation, we propose a principal component empirical likelihood (PCEL) methodology for tackling high-dimensional moment constraints in the spatial model. This approach innovatively transforms high-dimensional constraints on the scoring function into low-dimensional constraints while maximizing information retention. Theoretical analysis demonstrates that the PCEL ratio statistics asymptotically follow chi-squared distributions, enabling the construction of confidence regions for high-dimensional parameters in SARSAR models. Simulation results demonstrate that the PCEL method achieves coverage probabilities significantly closer to nominal confidence levels compared to both usual EL and modified EL approaches. Furthermore, PCEL maintains robust performance even in ultra-high-dimensional regimes where EL fails. Finally, we conduct an empirical analysis on a classical spatial dataset.