I'm investigating using a trimmed mean to measure the location of various distributions. The distributions sometimes are heavily contaminated and sometimes not. Usually they follow something similar to a log-normal or possibly mixed log-normal distribution, but often the data is "all over the place".
I've looked at the mean, 5% trimmed mean, 10% trimmed mean and 20% trimmed mean. For each I estimate the standard error using the bootstrap.
What I've found surprising though is that according to the bootstrap the mean often has a lower standard error than the 5% trimmed mean. So across a large number of datasets I have found that from the lowest standard error to the highest is 20% trimmed, 10% trimmed, mean, 5% trimmed.
Is this result atypical, or is it something that is commonly seen ? (Note that I am a beginner with respect to robust statistics and the bootstrap, so it is possible I'm making a fundamental conceptual mistake). Thanks for any hints.
Followup results: I reran the exercise but with much more data. In total there were around 4000 datasets I applied the bootstrap to. The results were as follows
technique number of times lowest std error mean 1867 5% trimmed 263 10% trimmed 430 20% trimmed 787 median 663
In this new data when the mean has the lowest standard error it is only better by a small amount, whereas when it does badly it performs really poorly. So when I look at the average standard error across all datasets for the different techniques the results are perhaps in line with what would be expected.
technique avg std error mean 4.51 5% trimmed 4.33 10% trimmed 4.05 20% trimmed 3.78 median 4.36