Variance of a Winsorized Mean When the Sample Contains Multiple Outliers

Abstract

In this note, we make use of some relationships between the product moments of order statistics in order to derive a computationally convenient formula for the variance of a general Winsorized mean. We then generalize this result to the case when multiple outliers are present in the sample. Formulas for the special case of multiple location-outlier and multiple scale-outlier models are deduced. Finally, we present three numerical examples to illustrate the use of the formulas derived here.

Keywords:

• Order statistics
• Linear estimator
• Robust estimator
• Winsorized mean
• Outliers
• Location-outlier model
• Scale-outlier model
• Product moments
• Recurrence relation