Adjusted Calibration Estimators for Sparse Spatial Data

We developed an adjusted calibration estimator for spatial data analysis where the units of a population N have low spatial density. The calibrated estimator is based on linear equations applied on auxiliary variables \(\mathbf {x_i}\) and constrained on known population total \(\textbf{X}\) . The linear model explains the relation between the study variable y and the auxiliary variables \(\mathbf {x_i}\) . In a context of spatial data analysis with low density we propose to adjust the calibrated estimator by a distance function. The Traveling Salesman Problem (TSP) is a basic routing problem stated for visit to P cities with the shortest closed tour. Different algorithms have been developed to resolve heuristically the TSP. This article developed a correction to the calibrated estimator based on a TSP. The performances of the adjusted estimator are evaluated using an application study on a forest landscape.