Comparison of the bias of trimmed and Winsorized means

ABSTRACT

We derive sharp upper and lower projection bounds on the bias of two-sided Winsorized means. To determine the projection of appropriate function, we consider new analytic condition which describes the form of the corresponding greatest convex minorant. Then we compare numerically obtained bounds for trimmed and Winsorized means. We conclude that if we have no information about the underlying distribution then Winsorized means are better than the trimmed ones.

KEYWORDS:

• Bias
• Hölder’s inequality
• Projection method
• Trimmed mean
• Winsorized mean

Mathematics Subject Classification:

• 62G30