Ordered Spatial Sampling by Means of the Traveling Salesman Problem

In recent years, spatial sampling has been the subject of a flourishing literature. Its use had become widespread due to the availability of topographical information about statistical units, especially in the environmental context. New algorithms enable us to take advantage of spatial locations directly. In this paper, we present a new way of using spatial information by using traditional sampling techniques as systematic sampling. By means of a famous optimization method, the Traveling Salesman Problem, it is possible to order the statistical units in a way that preserves the spatial correlation. Next ordered sampling methods are applied on the statistical units. Therefore we can render spatial some non-spatial methods. An economic application on real data is presented and different spatial and non-spatial methods are tested. Results are compared in terms of variance estimation and spatial balance, in order to establish the possibility of spatializing traditional sampling methods and of implementing them on data of different nature, among which economic ones.