For a location M-functional defined by
$$
\int\psi(x-T(F))\,dF(x)=0,
$$
its <influence function> is
$$
\operatorname{IF}(x;T,F)
=\frac{\psi(x-T(F))}
{\mathbb E_F[\psi'(X-T(F))]},
$$
provided the denominator is nonzero. A bounded score therefore gives a bounded influence function.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 223 / 3 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-223/3/a/solution