On Computation and Robustness Issues in Spatial Statistics

Overview

First, the effect of spatial covariance matrix ordering on parameter estimation via low-rank approximation is examined, demonstrating that careful ordering can yield higher computation efficiency without affecting accuracy. Next, the Maximum Lq-Likelihood Estimator (MLqE) is developed for replicated spatial datasets, showing superior robustness over the Maximum Likelihood Estimator when outliers are present. To extend its applicability to large-scale problems, a mixed-precision strategy, combined with a hierarchical precision scheme, is introduced to accelerate MLqE computations. Finally, a new method, the Maximum Composite Lq-Likelihood Estimator (MCLqE), is proposed by integrating MLqE with composite likelihood, enabling robust parameter estimation for single-replicate spatial data. Together, these contributions broaden the practical utility of robust spatial inference in both methodological and computational dimensions.