Geographically weighted regression model-calibration for finite population parameter estimation under two stage sampling design

Abstract

In many agricultural, forestry, environmental, and ecological surveys, data are often spatial in nature and exhibit spatial nonstationarity. A well-known method for addressing spatial nonstationarity and capturing the spatially varying relationships between different variables is Geographic Weighted Regression (GWR). The calibration approach is one of the most widely used techniques in sample surveys for incorporating the known population characteristics of auxiliary variables by changing the original sampling design weights. The model-calibration approach is an improvement on the conventional calibration approach that can handle a variety of assisting working models. Two-stage sampling is one of the most frequently used sampling strategies in large-scale sample surveys. In the present study, a couple of GWR model-calibration estimators were proposed under two-stage sampling, assuming the availability of population-level complete auxiliary information. Under a set of regularity assumptions, the asymptotic properties of the developed estimators have been evaluated such as design unbiasedness, model unbiasedness, approximate variance, and estimators of variances. The performance of the developed estimators has been compared with the existing estimators through a spatial simulation study and a design-based simulation based on real data. The performance of the proposed estimator was found to be more precise than the existing estimators under two-stage sampling.

Keywords:

• Geographically weighted regression
• Model-calibration
• Spatial nonstationarity
• Superpopulation

Mathematics Subject Classification:

• 62D05

Acknowledgments

The authors would like to thank the anonymous referees and the Editor for constructive comments and suggestions which led to the significant improvement in the manuscript. The first author would like to express his heartfelt gratitude to the ICAR-Indian Agricultural Statistics Research Institute, New Delhi, India and the Graduate School, ICAR-Indian Agricultural Research Institute, New Delhi, India, for providing lab facilities, real survey dataset and overall support to conduct the research work during his M.Sc. programme.

Disclosure statement

The authors have no competing financial or nonfinancial interests to declare that are relevant to the content of this article.