12. The definition of the percentage bend correlation coefficient, pb, involves a measure of scale, x, that

12. 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], where 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.