Spatial Regression With Multiplicative Errors, and Its Application With Lidar Measurements

TL;DR

This paper introduces a penalized modified least squares estimator for spatial regression with multiplicative errors, demonstrating its theoretical properties, superior performance in simulations, and successful application to LiDAR-based landslide surface estimation.

Contribution

It develops a novel estimator for spatial regression with multiplicative errors, providing theoretical validation and demonstrating practical effectiveness with LiDAR data.

Findings

Estimator outperforms existing methods in simulations

Provides asymptotic properties under increasing domain asymptotics

Successfully applied to real LiDAR data for landslide surface estimation

Abstract

Multiplicative errors in addition to spatially referenced observations often arise in geodetic applications, particularly in surface estimation with light detection and ranging (LiDAR) measurements. However, spatial 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 for surface estimation. 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.