Thus, demonstrating (9) amounts to showing E[χa(O,ˆra,α;η)] =O P(1/√n+R n).(11) We consider the following decomposition forE[χa(O,ˆra,α;η)]

Take the supremum of this bias structure over allrto boundE(χ a(ˆra,α,ˆη)−χ a(ˆra,α, η)) To begin, notice P(Y(a)∈ ˆCa(V)|S= 0)−(1−α) =P(R a(Y(a),V)≤ˆr a,α)|S= 0)−(1−α) =E[χ a(O,ˆra,α, η)]/P(S= 0),(10) where (10) holds since P(Ra(Y(a),V)≤r)|S · 2000