Generalised random tessellation stratified sampling over auxiliary spaces

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Abstract
Generalised Random Tessellation Stratified (GRTS) is a popular spatially balanced sampling design. GRTS can draw spatially balanced probability samples in two dimensions but has not been used to sample higher-dimensional auxiliary spaces. This article considers applying dimensionality reduction techniques to multidimensional auxiliary spaces to allow GRTS to be used to sample them. The aim is to improve the precision of GRTS-based estimators of population characteristics by incorporating auxiliary information into the GRTS sample. We numerically evaluate two dimensionality reduction techniques for equal and unequal probability samples on two spatial populations. Multipurpose surveys are also considered. Results show that GRTS samples from these two-dimensional spaces can improve the precision of GRTS over spatial coordinates.

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