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Generalised random tessellation stratified sampling over auxiliary spaces.

B L Robertson1, C J Price1, M Reale1

  • 1School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.

Journal of Applied Statistics
|December 5, 2025
PubMed
Summary
This summary is machine-generated.

Generalised Random Tessellation Stratified (GRTS) sampling can now incorporate higher-dimensional auxiliary data. Dimensionality reduction techniques enhance GRTS precision for complex spatial populations and multipurpose surveys.

Keywords:
Environmental samplingdimensionality reductionprincipal component analysisspatial balancet-SNEunequal probability

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Area of Science:

  • Spatial Statistics
  • Survey Methodology
  • Data Science

Background:

  • Generalised Random Tessellation Stratified (GRTS) is a widely used spatially balanced sampling design.
  • Current GRTS applications are limited to two-dimensional spatial sampling.
  • Incorporating multidimensional auxiliary information can improve estimation precision.

Purpose of the Study:

  • To adapt GRTS for sampling higher-dimensional auxiliary spaces using dimensionality reduction.
  • To enhance the precision of GRTS-based estimators by integrating auxiliary data.
  • To evaluate the effectiveness of dimensionality reduction techniques for GRTS.

Main Methods:

  • Application of dimensionality reduction techniques to multidimensional auxiliary spaces.
  • Numerical evaluation of two dimensionality reduction methods for GRTS.
  • Assessment of GRTS performance on two spatial populations with equal and unequal probability samples.
  • Consideration of multipurpose survey designs.

Main Results:

  • Dimensionality reduction enables GRTS to effectively sample higher-dimensional auxiliary spaces.
  • GRTS samples derived from reduced two-dimensional auxiliary spaces improved estimation precision compared to using spatial coordinates alone.
  • The evaluated techniques showed potential for enhancing multipurpose surveys.

Conclusions:

  • Dimensionality reduction is a viable strategy for extending GRTS to multidimensional auxiliary spaces.
  • Integrating auxiliary information via dimensionality reduction offers a significant improvement in GRTS precision.
  • This approach broadens the applicability of GRTS in complex survey designs.