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