In the previous post, we obtained the finite-sample Gaussian efficiency values of the sample median and the Harrell-Davis median. In this post, we extended these results and get the finite-sample Gaussian efficiency values of the trimmed Harrell-Davis median estimator based on the highest density interval of the width \(1/\sqrt{n}\).
Similarly to the previous experiment,
I have conducted a numerical simulation
which enumerates various sample sizes (2..100);
generates 1,000,000 samples from the normal distribution;
estimates the mean, the sample median (SM),
the Harrell-Davis median for these samples (HD),
and the trimmed Harrell-Davis median based on the highest density interval of size \(1/\sqrt{n}\) (THD-SQRT);
calculates the finite-sample relative efficiency of the sample median and the Harrell-Davis median
to the mean (the Gaussian efficiency).
Here are the results:
As we can see, THD-SQRT is less efficient than HD (which is the price of robustness),
but it is still more efficient than SM.