A simple two-step method for spatio-temporal design-based balanced sampling

  • Ramin Khavarzadeh
  • Mohsen Mohammadzadeh
  • Jorge Mateu
Original Paper


We introduce a two-step method to perform spatio-temporal balanced sampling in a design-based approach. For populations with spatio-temporal trends and with anisotropic effects in the variable of interest, the prediction can be further improved by selecting samples that are well spread over the entire population in space and time. We control the spread of the sample over the population by using the volume of the corresponding three-dimensional Voronoi tessellation. Indeed, spatio-temporal design-based balanced sampling is even more efficient under the presence of a trend and anisotropic effects. We present an intensive simulation study comparing our method to other available methods for spatio-temporal sampling. Finally, we analyze real data by sampling from a population of temperature stations over six European countries.


Balanced sampling Design-based sampling Spatio-temporal sampling 



The authors are thankful to the referees for their many helpful comments that greatly improved this paper. We also wish to acknowledge for the support from Ordered and Spatial Data Center of Excellence of the Ferdowsi University of Mashhad.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Ramin Khavarzadeh
    • 1
  • Mohsen Mohammadzadeh
    • 1
  • Jorge Mateu
    • 2
  1. 1.Department of StatisticsTarbiat Modares UniversityTehranIran
  2. 2.Department of MathematicsUniversity Jaume ICastellónSpain

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