In the previous post, we introduced the trimmed Hodges-Lehman location estimator. For a sample \(\mathbf{x} = \{ x_1, x_2, \ldots, x_n \}\), it is defined as follows:

\[\operatorname{THL}(\mathbf{x}, k) = \underset{k < i < j \leq n - k}{\operatorname{median}}\biggl(\frac{x_{(i)} + x_{(j)}}{2}\biggr). \]

We also derived the exact expression for its asymptotic and finite-sample breakdown point values. In this post, we explore its Gaussian efficiency.

### Gaussian efficiency

Here is the plot with Gaussian efficiency values for \(3 \leq n \leq 25\):

### References

**[Hodges1963]**

Hodges, J. L., and E. L. Lehmann. 1963. Estimates of location based on rank tests. The Annals of Mathematical Statistics 34 (2):598–611.

DOI: 10.1214/aoms/1177704172