Winsorising

Winsorising or Winsorization is the transformation of statistics by transforming extreme values in the statistical data, and is named for the engineer-turned-biostatistician Charles P. Winsor (1895–1951).

The distribution of many statistics can be heavily influenced by outliers. 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 estimators are usually more robust to outliers than their unwinsorised counterparts.

Distinction from trimming

Note that Winsorizing is not equivalent to simply excluding data, which is a simpler procedure, called trimming.

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).

For example, a Winsorized mean is not the same as a truncated mean: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.

More formally, they are distinct because the order statistics are not independent.

References

* "Simplified Estimation from Censored Normal Samples", W. J. Dixon, The Annals of Mathematical Statistics, 31, pp. 385-391, 1960
* "The Future of Data Analysis", J. W. Tukey, The Annals of Mathematical Statistics, 33, p. 18, 1962