Spatiotemporal Balanced Sampling Design for Longitudinal Area Surveys

  • Zhonglei Wang
  • Zhengyuan ZhuEmail author


A spatially balanced sample can produce good estimates of finite population quantities when the study variable is dependent over a spatial region with respect to a super-population model. In many longitudinal surveys for monitoring natural resources, annual samples are taken in space to estimate both annual status and annual change. In this paper, we propose a spatiotemporal balanced sampling design with a repeated panel such that the sample for each year is spatially balanced, and the sample combined from consecutive years is also spatially balanced. We propose design-based regression estimators of the annual status and change, and the corresponding variance estimators are also derived. Simulation studies show that the spatial balance of a sample generated by the proposed spatiotemporal balanced sampling design is good, and design-based regression estimators work well. The proposed spatiotemporal balanced sampling design is tested on data from the National Resources Inventory rangeland on-site survey conducted in Texas from 2009 to 2013. For the study variable “average soil aggregate stability,” the proposed sampling design and estimators are shown to have better performance compared with the original sample and estimators. Although the spatiotemporal balanced sampling design is proposed in a two-dimensional space, it can be generalized to higher dimensions easily.

Supplementary materials accompanying this paper appear online.


Annual change Annual status Environmental survey Regression estimator Variance estimator 



We are grateful to the associate editor and three referees for the detailed and constructive comments. This research was supported in part by the Natural Resources Conservation Service of the U.S. Department of Agriculture. By personal communication, Anton Grafström independently developed the hierarchical local pivotal method and used it to split the Swedish NFI sample for the years 2018–2022; see function hlpm of Grafström and Lisic (2018) for details.

Supplementary material

13253_2019_350_MOESM1_ESM.pdf (168 kb)
Supplementary material 1 (pdf 168 KB)


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Copyright information

© International Biometric Society 2019

Authors and Affiliations

  1. 1.MOE Key Laboratory of Econometrics, Wang Yanan Institute for Studies in Economics and School of EconomicsXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Department of StatisticsIowa State UniversityAmesUSA

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