# 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**

### 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**

### 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