# Trimmed estimator

trimmedtrimming
In statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation.wikipedia
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### Robust statistics

robustbreakdown pointrobustness
This is generally done to obtain a more robust statistic, and the extreme values are considered outliers.
Trimmed estimators and Winsorised estimators are general methods to make statistics more robust.

### Median

averagesample medianmedian-unbiased estimator
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.
(In more technical terms, this interprets the median as the fully trimmed mid-range).

### L-estimator

L-estimation
Trimmed estimators involving only linear combinations of points are examples of L-estimators.
A more detailed list of examples includes: with a single point, the maximum, the minimum, or any single order statistic or quantile; with one or two points, the median; with two points, the mid-range, the range, the midsummary (trimmed mid-range, including the midhinge), and the trimmed range (including the interquartile range and interdecile range); with three points, the trimean; with a fixed fraction of the points, the trimmed mean (including interquartile mean) and the Winsorized mean; with all points, the mean.

### Truncation (statistics)

truncationstatistical truncationtruncated
In statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation.
Trimmed estimator

### Truncated mean

trimmed meanmodified mean
For instance, the 5% trimmed mean is obtained by taking the mean of the 5% to 95% range. Interquartile mean, the 25% trimmed mean
As with other trimmed estimators, the main advantage of the trimmed mean is robustness and higher efficiency for mixed distributions and heavy-tailed distribution (like the Cauchy distribution), at the cost of lower efficiency for some other less heavily-tailed distributions (such as the normal distribution).

### Midhinge

Midhinge, the 25% trimmed mid-range
Equivalently, it is the 25% trimmed mid-range or 25% midsummary; it is an L-estimator.

### Interquartile range

inter-quartile rangebelowinterquartile
Interquartile range, the 25% trimmed range
It is a trimmed estimator, defined as the 25% trimmed range, and is a commonly used robust measure of scale.

### Mid-range

midsummarymidrangehalf-range
Midhinge, the 25% trimmed mid-range
A trimmed midrange is known as a – the n% trimmed midrange is the average of the n% and (100−n)% percentiles, and is more robust, having a breakdown point of n%. In the middle of these is the midhinge, which is the 25% midsummary.

### Robust measures of scale

Qn estimatorrobust estimator of dispersionrobust measure of scale
When estimating a scale parameter, using a trimmed estimator as a robust measures of scale, such as to estimate the population variance or population standard deviation, one generally must multiply by a scale factor to make it an unbiased consistent estimator; see scale parameter: estimation.
One of the most common robust measures of scale is the interquartile range (IQR), the difference between the 75th percentile and the 25th percentile of a sample; this is the 25% trimmed range, an example of an L-estimator.

### Winsorizing

Winsorised estimatorswinsorized
Winsorising, a related technique
Winsorized estimators are usually more robust to outliers than their more standard forms, although there are alternatives, such as trimming, that will achieve a similar effect.

### Statistics

statisticalstatistical analysisstatistician
In statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation.

### Estimator

estimatorsestimateestimates
In statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation.

### Maxima and minima

maximumminimumlocal maximum
In statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation.

### Outlier

outliersconservative estimateirregularities
This is generally done to obtain a more robust statistic, and the extreme values are considered outliers.

### Efficiency (statistics)

efficientefficiencyinefficient
Trimmed estimators also often have higher efficiency for mixture distributions and heavy-tailed distributions than the corresponding untrimmed estimator, at the cost of lower efficiency for other distributions, such as the normal distribution.

### Mixture distribution

mixturemixture densitydensity mixture
Trimmed estimators also often have higher efficiency for mixture distributions and heavy-tailed distributions than the corresponding untrimmed estimator, at the cost of lower efficiency for other distributions, such as the normal distribution.

### Heavy-tailed distribution

heavy tailsheavy-tailedheavy tail
Trimmed estimators also often have higher efficiency for mixture distributions and heavy-tailed distributions than the corresponding untrimmed estimator, at the cost of lower efficiency for other distributions, such as the normal distribution.

### Normal distribution

normally distributednormalGaussian
Trimmed estimators also often have higher efficiency for mixture distributions and heavy-tailed distributions than the corresponding untrimmed estimator, at the cost of lower efficiency for other distributions, such as the normal distribution.

### Quantile

quantilesquintiletertile
Quantiles can be thought of as trimmed maxima or minima: for instance, the 5th percentile is the 5% trimmed minimum.

### Percentile

percentiles50th percentile85th percentile speed
Quantiles can be thought of as trimmed maxima or minima: for instance, the 5th percentile is the 5% trimmed minimum.

### Location parameter

locationlocation modelshift parameter
Trimmed estimators used to estimate a location parameter include:

### Scale parameter

scalerate parameterestimation
When estimating a scale parameter, using a trimmed estimator as a robust measures of scale, such as to estimate the population variance or population standard deviation, one generally must multiply by a scale factor to make it an unbiased consistent estimator; see scale parameter: estimation. Trimmed estimators used to estimate a scale parameter include:

### Interquartile mean

interquartile
Interquartile mean, the 25% trimmed mean

### Range (statistics)

rangerangingsample range
Interquartile range, the 25% trimmed range

### Interdecile range

Interdecile range, the 10% trimmed range