Examples
The median is the most trimmed statistic (nominally 50%), as it discards all but the most central data, and equals the fully trimmed mean – or indeed fully trimmed mid-range, or (for odd size data sets) the fully trimmed maximum or minimum. Likewise, no degree of trimming has any effect on the median – a trimmed median is the median – because trimming always excludes an equal number of the lowest and highest values.
Quantiles can be thought of as trimmed maxima or minima: for instance, the 5th percentile is the 5% trimmed minimum.
Trimmed estimators used to estimate a location parameter include:
- Trimmed mean
- Modified mean, discarding the minimum and maximum values
- Interquartile mean, the 25% trimmed mean
- Midhinge, the 25% trimmed mid-range
Trimmed estimators used to estimate a scale parameter include:
- Interquartile range, the 25% trimmed range
- Interdecile range, the 10% trimmed range
Trimmed estimators which only involve linear combinations of points are examples of L-estimators.
Read more about this topic: Trimmed Estimator
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