The definition of the percentage bend correlation coefficient, ρpb, involves a measure of scale, ω x , that is estimated with ωˆ = W(m), where W i = |Xi − M x | and m = [(1 − β)n], 0 ≤ β ≤ .5. Note...

The definition of the percentage bend correlation coefficient, ρpb, involves a measure of scale, ω_x, that is estimated with ωˆ = W(m), where W_i
= |Xi − M_x| and m = [(1 − β)n], 0 ≤ β ≤ .5. Note that this measure of scale is defined even when .5 <> 0. Argue that the finite-sample breakdown point of this estimator is maximized when β = .5