The definition of the percentage bend correlation coefficient, pb, involves a measure of scale, x , that is estimated with = W(m) , where

The definition of the percentage bend correlation coefficient, ρpb, involves a measure of scale, ωx , that is estimated with ωˆ = W(m)

, where Wi = |Xi − Mx | and m = [(1−β)n], and 0 ≤ β ≤ 0.5. Note that this measure of scale is defined even when 0.5 < β < 1 provided that m > 0. Argue that the finite sample breakdown point of this estimator is maximized when β = 0.5.