Abstract: In areal surveys, one-per-stratum sampling is commonly used since it achieves spatial balance and improves estimation efficiency. The downside of such a design is that it is challenging to have a good variance estimator. In this paper, we propose a generalized one-per-stratum sampling design to generate a spatially balanced sample. The sample is used to get an M-estimator of the parameters in a spatial linear regression model, and the corresponding variance is estimated by a resampling method. Asymptotic properties of the M-estimator are investigated under the proposed one-per-stratum sampling design. Simulation studies show that the proposed one-per-stratum sampling design achieves good spatial balance, and the M-estimator is more efficient compared with existing designs. The resampling method is applied to investigate the relationship between soil erosion and slope in Iowa using a recent sample from the National Resources Inventory survey.

Key words and phrases: Asymptotics, M-estimator, spatial block bootstrap, spatially balanced sampling, survey variance estimation.