Winsorising
Encyclopedia
Winsorising or Winsorization is the transformation of statistic
s by limiting extreme values in the statistical
data to reduce the effect of possibly spurious outliers. It is named after the engineer-turned-biostatistician Charles P. Winsor (1895–1951). The effect is the same as clipping
in signal processing.
The distribution of many statistic
s can be heavily influenced by outlier
s. A typical strategy is to set all outliers to a specified percentile
of the data; for example, a 90% Winsorisation would see all data below the 5th percentile set to the 5th percentile, and data above the 95th percentile set to the 95th percentile.
Winsorised estimator
s are usually more robust
to outliers than their more standard forms, although there are alternatives, such as trimming
, that will achieve a similar effect.
The 5th percentile lies between -40 and 2, while the 95th percentile lies between 101 and 153. (Values shown in bold.)
Then a 90% Winsorisation would result in the following:
.
In a trimmed estimator, the extreme values are discarded; in a Winsorized estimator, the extreme values are instead replaced by certain percentiles (the trimmed minimum and maximum).
Thus a Winsorized mean
is not the same as a truncated mean
.
For instance, the 5% trimmed mean is the average of the 5th to 95th percentile of the data, while the 90% Winsorised mean sets the bottom 5% to the 5th percentile, the top 5% to the 95th percentile, and then averages the data. In the previous example the trimmed mean would be obtained from the smaller set:
More formally, they are distinct because the order statistics are not independent.
Statistic
A statistic is a single measure of some attribute of a sample . It is calculated by applying a function to the values of the items comprising the sample which are known together as a set of data.More formally, statistical theory defines a statistic as a function of a sample where the function...
s by limiting extreme values in the statistical
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
data to reduce the effect of possibly spurious outliers. It is named after the engineer-turned-biostatistician Charles P. Winsor (1895–1951). The effect is the same as clipping
Clipping (signal processing)
Clipping is a form of distortion that limits a signal once it exceeds a threshold. Clipping may occur when a signal is recorded by a sensor that has constraints on the range of data it can measure, it can occur when a signal is digitized, or it can occur any other time an analog or digital signal...
in signal processing.
The distribution of many statistic
Statistic
A statistic is a single measure of some attribute of a sample . It is calculated by applying a function to the values of the items comprising the sample which are known together as a set of data.More formally, statistical theory defines a statistic as a function of a sample where the function...
s can be heavily influenced by outlier
Outlier
In statistics, an outlier is an observation that is numerically distant from the rest of the data. Grubbs defined an outlier as: An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs....
s. A typical strategy is to set all outliers to a specified percentile
Percentile
In statistics, a percentile is the value of a variable below which a certain percent of observations fall. For example, the 20th percentile is the value below which 20 percent of the observations may be found...
of the data; for example, a 90% Winsorisation would see all data below the 5th percentile set to the 5th percentile, and data above the 95th percentile set to the 95th percentile.
Winsorised estimator
Estimator
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule and its result are distinguished....
s are usually more robust
Robust statistics
Robust statistics provides an alternative approach to classical statistical methods. The motivation is to produce estimators that are not unduly affected by small departures from model assumptions.- Introduction :...
to outliers than their more standard forms, although there are alternatives, such as trimming
Trimmed estimator
Given an estimator, a trimmed estimator is obtained by excluding some of the extreme values. This is generally done to obtain a more robust statistic: the extreme values are considered outliers....
, that will achieve a similar effect.
Example
Consider the data set consisting of:The 5th percentile lies between -40 and 2, while the 95th percentile lies between 101 and 153. (Values shown in bold.)
Then a 90% Winsorisation would result in the following:
Distinction from trimming
Note that Winsorizing is not equivalent to simply excluding data, which is a simpler procedure, called trimmingTrimmed estimator
Given an estimator, a trimmed estimator is obtained by excluding some of the extreme values. This is generally done to obtain a more robust statistic: the extreme values are considered outliers....
.
In a trimmed estimator, the extreme values are discarded; in a Winsorized estimator, the extreme values are instead replaced by certain percentiles (the trimmed minimum and maximum).
Thus a Winsorized mean
Winsorized mean
A Winsorized mean is a Winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean...
is not the same as a truncated mean
Truncated mean
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both.For...
.
For instance, the 5% trimmed mean is the average of the 5th to 95th percentile of the data, while the 90% Winsorised mean sets the bottom 5% to the 5th percentile, the top 5% to the 95th percentile, and then averages the data. In the previous example the trimmed mean would be obtained from the smaller set:
More formally, they are distinct because the order statistics are not independent.