A comparison of sampling grids, cut-off distance and type of residuals in parametric variogram estimation

ABSTRACT

In spatial statistics, the correct identification of a variogram model when fitted to an empirical variogram depends on many factors. Here, simulation experiments show fitting based on the variogram cloud is preferable to that based on Matheron's and Cressie–Hawkins empirical variogram estimators. For correct model specification, a number of models should be fitted to the empirical variogram using a grid of cut-off values, and recommendations are given for best choice. A design where roughly half the maximum distance between points equals the practical range works well for correct variogram identification of any model, with varying nugget sizes and sample sizes.

KEYWORDS:

• Matérn
• Practical range
• Studentized residuals
• Variogram cloud
• Variogram model fitting

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H11
• 62K05

Acknowledgments

We would like to thank the referees for helpful comments that improved this manuscript. Renhao Jin is supported by a Chinese Science Council (CSC) Government Scholarship (to UCD).