Spatial regression with multiplicative errors, and its application with LiDAR measurements

Multiplicative errors in addition to spatially referenced observations often arise in geodetic applications, particularly with light detection and ranging (LiDAR) measurements. However, regression involving multiplicative errors remains relatively unexplored in such applications. In this regard, we present a penalized modified least squares estimator to handle the complexities of a multiplicative error structure while identifying significant variables in spatially dependent observations. The proposed estimator can be also applied to classical additive error spatial regression. By establishing asymptotic properties of the proposed estimator under increasing domain asymptotics with stochastic sampling design, we provide a rigorous foundation for its effectiveness. A comprehensive simulation study confirms the superior performance of our proposed estimator in accurately estimating and selecting parameters, outperforming existing approaches. To demonstrate its real-world applicability, we employ our proposed method, along with other alternative techniques, to estimate a rotational landslide surface using LiDAR measurements. The results highlight the efficacy and potential of our approach in tackling complex spatial regression problems involving multiplicative errors.