Winsorized mean

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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. It involves the calculation of the mean after winsorizing -- replacing given parts of a probability distribution or sample at the high and low end with the most extreme remaining values,[1] typically doing so for an equal amount of both extremes; often 10 to 25 percent of the ends are replaced. The winsorized mean can equivalently be expressed as a weighted average of the truncated mean and the quantiles at which it is limited, which corresponds to replacing parts with the corresponding quantiles.

Advantages[edit]

The winsorized mean is a useful estimator because it is less sensitive to outliers than the mean but will still give a reasonable estimate of central tendency or mean for almost all statistical models. In this regard it is referred to as a robust estimator.

Drawbacks[edit]

The winsorized mean uses more information from the distribution or sample than the median. However, unless the underlying distribution is symmetric, the winsorized mean of a sample is unlikely to produce an unbiased estimator for either the mean or the median.

Example[edit]

  • For a sample of 10 numbers (from x1, the smallest, to x10 the largest) the 10% winsorized mean is
The key is in the repetition of x2 and x9: the extras substitute for the original values x1 and x10 which have been discarded and replaced.
This is equivalent to a weighted average of 0.1 times the 5th percentile (x2), 0.8 times the 10% trimmed mean, and 0.1 times the 95th percentile (x9).

Notes[edit]

  1. ^ Dodge, Y (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9 (entry for "winsorized estimation")

References[edit]