Now let
$$
\psi_{a,b}(x)
=\left[\Delta\left(x-\frac{\theta_0+\theta_1}{2}\right)\right]_a^b.
$$
Then
$$
\operatorname{IF}_{\rm test}(x;S,F_\theta)
=\psi_{a,b}(x)-\mathbb E_{F_\theta}\psi_{a,b}(X).
$$
Since $a\leq\psi_{a,b}(x)\leq b$, this influence function is bounded for both hypotheses. Clipping the log-likelihood contribution prevents one extreme observation from having unbounded effect on the statistic.


Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 223 / 3 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-223/3/c/solution