Generalised random tessellation stratified sampling over auxiliary spaces

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.