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