Thoughts on Geothmetic Meandian

Let us consider xkcd.com/2435:

While this strip may look like a joke, it contains an interesting idea for [Research] Resistance to the low-density regions.

The classic “simple” estimators typically have poor resistance against low-density regions around the breakdown point. The wider the low-density region, the lower the corresponding statistical efficiency. Any kind of aggregation allows mitigate the error magnitude when we hit a low-density region. Potentially, it can reduce the overall efficiency in high-density regions, but I doubt that we would experience a noticeable efficiency loss in majority of simple cases.

The geothmetic meandian does not feel useful, but what if we combine the median with the The Hodge-Lehmann Estimator? Or the Shamos estimator with the Rousseeuw-Croux scale estimator? More interesting experiments are coming…