Robust Getis-Ord Gi* Statistic
Also known as: Robust Gi*, Robust local Gi star, outlier-resistant hot spot analysis, robust local spatial autocorrelation Gi*
The Robust Getis-Ord Gi* statistic extends the classical Gi* hot-spot measure to handle outliers in spatial data. By using robust estimators of the mean and variance — such as trimmed means, medians, or down-weighted influential observations — it identifies statistically significant spatial clusters of high or low values even when the attribute distribution contains extreme values that would distort the standard Gi*.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use Robust Getis-Ord Gi* when you suspect that a small number of extreme attribute values (e.g., a single very high crime count, an anomalously large income figure) are distorting hot-spot results from the standard Gi*. It is appropriate when exploratory diagnostics show skewed or heavy-tailed distributions, or when a sensitivity analysis reveals that classical Gi* results shift substantially after removing a few observations. It is the right choice for crime mapping, disease surveillance, ecological surveys, and real-estate analysis where outlying values are common. Do not use it as a blanket replacement for the standard Gi* when data are well-behaved; the added complexity is unnecessary. Avoid it when the dataset is very small (fewer than ~30 locations), since robust estimators themselves become unstable.
Strengths & limitations
- Resistant to the distorting influence of extreme attribute values that inflate or deflate the global mean and variance used in the standard Gi*.
- Preserves the intuitive hot-spot/cold-spot interpretation of the original Getis-Ord Gi* while improving reliability in skewed or contaminated datasets.
- Compatible with permutation-based inference, which avoids the normality assumption and yields valid p-values even for non-Gaussian attribute distributions.
- Applicable to both point and areal data, with flexibility in the spatial weights specification (distance-based, contiguity-based, or k-nearest-neighbours).
- Diagnostic comparison with the standard Gi* reveals which clusters are genuine spatial patterns versus artefacts of outliers.
- No single universally agreed-upon robust variant exists; the choice of trimming proportion or M-estimator introduces analyst discretion and affects results.
- Robust estimators require larger samples than the standard Gi* to achieve stable estimates; results can be unreliable with fewer than about 30 spatial units.
- Computationally more intensive than the standard Gi*, especially when using iterative M-estimators or permutation inference on large grids.
- Interpreting the degree of robustness introduced (how much trimming, which estimator) requires familiarity with robust statistics beyond typical GIS workflows.
- Software implementations vary; many GIS platforms offer only the classical Gi*, requiring custom scripting in R or Python for robust variants.
Frequently asked
How does Robust Gi* differ from the standard Getis-Ord Gi*?
The standard Gi* uses the global mean and standard deviation of all attribute values in its z-score denominator. If a few extreme values inflate or deflate those statistics, every location's z-score is affected. The robust variant replaces the sensitive global mean and variance with resistant alternatives — trimmed means, medians, or M-estimators — so that outliers have diminished influence on the overall clustering assessment.
Which robust estimator should I choose — trimmed mean, median, or M-estimator?
For moderate skewness, a 5–10% symmetric trimming of the global distribution is a practical starting point. The median and MAD offer the highest breakdown point (50%) but sacrifice efficiency for nearly normal data. M-estimators (e.g., Huber or Tukey bisquare) adaptively down-weight outliers and offer a good bias-variance trade-off. Sensitivity-test at least two choices and report both; if results agree, the specific choice matters little.
Can I run Robust Gi* in standard GIS software like ArcGIS or QGIS?
Standard hot-spot tools in ArcGIS (Optimized Hot Spot Analysis) and QGIS implement the classical Gi* and do not offer built-in robust variants. You can implement Robust Gi* in R (spdep + robustbase) or Python (PySAL / esda), then import the resulting z-scores and p-values back into GIS for mapping.
How do I know whether to use Robust Gi* or the standard Gi*?
Compute both and compare the maps. Also inspect the attribute distribution: significant right-skew, a kurtosis well above 3, or influential-observation diagnostics flagging a small number of extreme values all argue for the robust variant. If the two maps are nearly identical, use the simpler standard Gi*.
Does using a permutation test make robustness adjustments unnecessary?
Not fully. Permutation inference removes the normality assumption by building an empirical null distribution, which helps with inference validity. However, it does not change the z-score numerator or denominator; extreme values still distort the global mean and variance used to compute the test statistic itself. Robust estimators address the statistic's construction, while permutation addresses its distribution — ideally, use both together.
Sources
- Getis, A., & Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis, 24(3), 189–206. DOI: 10.1111/j.1538-4632.1992.tb00261.x ↗
- Anselin, L., & Liu, X. (2010). Spatial panel econometrics. In Handbook of Applied Economic Statistics. Robust spatial statistics variants are discussed in the context of outlier-resistant local indicators. See also: Anselin, L. (2018). A local indicator of multivariate spatial association. Geographical Analysis, 51(2), 133–150. link ↗
How to cite this page
ScholarGate. (2026, June 3). Robust Getis-Ord Gi* Statistic. ScholarGate. https://scholargate.app/en/spatial-analysis/robust-getis-ord-gi
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Hot Spot AnalysisSpatial analysis↔ compare
- Local Getis-Ord Gi*Spatial analysis↔ compare
- Local Moran's ISpatial analysis↔ compare
- Robust Local Indicators of Spatial AssociationSpatial analysis↔ compare
- Robust Spatial AutocorrelationSpatial analysis↔ compare