Testing nonparametric statistical functionals with applications to rank tests

1. P. 74. Substitute the last seven lines by: There exists a unique gradient ̃ ∈ L2 (P0) with smallest L2 (P0)-norm such that ̇ = ̃ + (̇ − ̃) and (̇ − ̃) is orthogonal with respect to {g− h : g; h ∈ T (P0;P)}. Actually, ̃ is the orthogonal projection of ̇ on the L2 (P0)-closure of the latter space. 2. In Theorem 3(b), Corollary 3.3, and A(ii), p. 78 the following assumption is needed (which trivially holds for all concrete examples under consideration). Suppose that ̃ ∈ T (P0;P) holds.