Finite-sample Gaussian efficiency of the trimmed Harrell-Davis median estimator

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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.



The source code of this post and all the relevant files are available on GitHub.
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